diff --git a/CHANGELOG.md b/CHANGELOG.md
index d61347b..3f4454c 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,3 +1,9 @@
+main
+------
+
+* Emit the scripts and stylesheets that `index.html` points outside the build (a CDN, a font service) as they are, instead of failing to resolve them against the build output
+* Ignore `<script>` tags without a `src` (an inline script) when collecting the build's scripts
+
 0.9.0
 ------
 
diff --git a/app/helpers/ember_cli_rails_assets_helper.rb b/app/helpers/ember_cli_rails_assets_helper.rb
index 745e9f2..8ba8bdd 100644
--- a/app/helpers/ember_cli_rails_assets_helper.rb
+++ b/app/helpers/ember_cli_rails_assets_helper.rb
@@ -1,6 +1,7 @@
 require "ember_cli/assets/errors"
 require "ember_cli/assets/lookup"
 require "ember_cli/assets/paths"
+require "ember_cli/assets/url"
 
 module EmberCliRailsAssetsHelper
   def include_ember_script_tags(name, prepend: "")
@@ -39,7 +40,7 @@ def include_ember_stylesheet_tags(name, prepend: "")
     assets = EmberCli::Assets::Lookup.new(app)
 
     assets.stylesheet_assets.
-      map { |src| [prepend, src].join }.
+      map { |src| mount_asset(src, prepend) }.
       map { |src| %{<link rel="stylesheet" href="#{src}">}.html_safe }.
       inject(&:+)
   end
@@ -69,11 +70,21 @@ def classic_ember_script_tags(app, prepend)
     assets = EmberCli::Assets::Lookup.new(app)
 
     assets.javascript_assets.
-      map { |src| [prepend, src].join }.
+      map { |src| mount_asset(src, prepend) }.
       map { |src| %{<script src="#{src}"></script>}.html_safe }.
       inject(&:+)
   end
 
+  # `prepend` mounts the build's assets onto a path (or another host), so it only applies to the URLs that point into the build.
+  # Assets hosted elsewhere (a CDN, a font service) are already absolute.
+  def mount_asset(src, prepend)
+    if EmberCli::Assets::Url.remote?(src)
+      src
+    else
+      [prepend, src].join
+    end
+  end
+
   # Vite builds boot from ES modules declared in dist/index.html, so extract
   # the tags required for startup (including the config meta tag and
   # stylesheets) and remap root-absolute paths onto the mount point.
diff --git a/lib/ember_cli/assets/asset_map.rb b/lib/ember_cli/assets/asset_map.rb
index 1b21187..e83c665 100644
--- a/lib/ember_cli/assets/asset_map.rb
+++ b/lib/ember_cli/assets/asset_map.rb
@@ -1,5 +1,6 @@
 require 'nokogiri'
 require "ember_cli/assets/errors"
+require "ember_cli/assets/url"
 
 module EmberCli
   module Assets
@@ -13,25 +14,35 @@ def initialize(name:, asset_map:, index_html:)
       def javascripts
         assert_asset_map!
 
-        Nokogiri::HTML(index_html.read).css('script').map {|s|
-          filename = File.basename(s['src'])
-          asset_matching(/#{Regexp.escape(filename)}\z/)
-        }
+        document.css('script').filter_map { |script| asset_for(script['src']) }
       end
 
       def stylesheets
         assert_asset_map!
 
-        Nokogiri::HTML(index_html.read).css('link[rel="stylesheet"]').map {|s|
-          filename = File.basename(s['href'])
-          asset_matching(/#{Regexp.escape(filename)}\z/)
-        }
+        document.css('link[rel="stylesheet"]').filter_map { |link| asset_for(link['href']) }
       end
 
       private
 
       attr_reader :name, :asset_map, :index_html
 
+      def document
+        @document ||= Nokogiri::HTML(index_html.read)
+      end
+
+      # Assets hosted outside the build (a CDN, a font service) have no entry in the asset map, so their URL is emitted untouched.
+      # A tag without a URL (an inline `<script>`) references no asset at all.
+      def asset_for(url)
+        if url.to_s.empty?
+          nil
+        elsif Url.remote?(url)
+          url
+        else
+          asset_matching(/#{Regexp.escape(File.basename(url))}\z/)
+        end
+      end
+
       def asset_matching(regex)
         matching_asset = files.detect { |asset| asset =~ regex }
 
diff --git a/lib/ember_cli/assets/url.rb b/lib/ember_cli/assets/url.rb
new file mode 100644
index 0000000..780691a
--- /dev/null
+++ b/lib/ember_cli/assets/url.rb
@@ -0,0 +1,14 @@
+module EmberCli
+  module Assets
+    # URLs in a built `index.html` either point into the build output or somewhere else entirely (a CDN, a font service).
+    # Only the former are resolved against the build and mounted onto the Rails application.
+    module Url
+      # Matches a URL that resolves outside the build: one carrying a scheme (`https://example.com/app.css`, `data:…`), and a protocol-relative one (`//example.com/app.css`).
+      REMOTE = %r{\A(?:[a-zA-Z][a-zA-Z0-9+.\-]*:|//)}
+
+      def self.remote?(url)
+        REMOTE.match?(url.to_s)
+      end
+    end
+  end
+end
diff --git a/spec/helpers/ember_cli_rails_assets_helper_spec.rb b/spec/helpers/ember_cli_rails_assets_helper_spec.rb
index 7c0ce51..5a185e7 100644
--- a/spec/helpers/ember_cli_rails_assets_helper_spec.rb
+++ b/spec/helpers/ember_cli_rails_assets_helper_spec.rb
@@ -42,6 +42,32 @@
         expect(tags).to include(%{src="//cdn.example.com/protocol-relative.js"})
       end
     end
+
+    context "when the application is a classic build" do
+      it "mounts the build's scripts onto `prepend`, leaving the ones hosted elsewhere untouched" do
+        app = instance_double(EmberCli::App, build: true, dev_server?: false)
+        paths = instance_double(EmberCli::Assets::Paths, vite?: false)
+        lookup = instance_double(
+          EmberCli::Assets::Lookup,
+          javascript_assets: [
+            "assets/vendor-abc123.js",
+            "https://cdn.example.com/analytics.js",
+            "//cdn.example.com/protocol-relative.js",
+          ],
+        )
+        allow(EmberCli).to receive(:[]).with(:frontend).and_return(app)
+        allow(EmberCli::Assets::Paths).
+          to receive(:new).with(app).and_return(paths)
+        allow(EmberCli::Assets::Lookup).
+          to receive(:new).with(app).and_return(lookup)
+
+        tags = helper.include_ember_script_tags(:frontend, prepend: "http://example.com/")
+
+        expect(tags).to include(%{src="http://example.com/assets/vendor-abc123.js"})
+        expect(tags).to include(%{src="https://cdn.example.com/analytics.js"})
+        expect(tags).to include(%{src="//cdn.example.com/protocol-relative.js"})
+      end
+    end
   end
 
   describe "#include_ember_stylesheet_tags" do
@@ -74,5 +100,31 @@
         )
       end
     end
+
+    context "when the application is a classic build" do
+      it "mounts the build's stylesheets onto `prepend`, leaving the ones hosted elsewhere untouched" do
+        app = instance_double(EmberCli::App, build: true, dev_server?: false)
+        paths = instance_double(EmberCli::Assets::Paths, vite?: false)
+        lookup = instance_double(
+          EmberCli::Assets::Lookup,
+          stylesheet_assets: [
+            "assets/vendor-abc123.css",
+            "https://fonts.example.com/css?family=Frontend",
+            "//fonts.example.com/protocol-relative.css",
+          ],
+        )
+        allow(EmberCli).to receive(:[]).with(:frontend).and_return(app)
+        allow(EmberCli::Assets::Paths).
+          to receive(:new).with(app).and_return(paths)
+        allow(EmberCli::Assets::Lookup).
+          to receive(:new).with(app).and_return(lookup)
+
+        tags = helper.include_ember_stylesheet_tags(:frontend, prepend: "http://example.com/")
+
+        expect(tags).to include(%{href="http://example.com/assets/vendor-abc123.css"})
+        expect(tags).to include(%{href="https://fonts.example.com/css?family=Frontend"})
+        expect(tags).to include(%{href="//fonts.example.com/protocol-relative.css"})
+      end
+    end
   end
 end
diff --git a/spec/lib/ember_cli/assets/asset_map_spec.rb b/spec/lib/ember_cli/assets/asset_map_spec.rb
index b9234c7..fd26789 100644
--- a/spec/lib/ember_cli/assets/asset_map_spec.rb
+++ b/spec/lib/ember_cli/assets/asset_map_spec.rb
@@ -29,6 +29,55 @@
       ])
     end
 
+    it "passes scripts hosted outside the build through untouched" do
+      asset_map = {
+        "assets" => {
+          "bar.js" => "bar-abc123.js",
+        },
+        "prepend" => "foo/",
+      }
+      index_html = StringIO.new(<<~HTML)
+        <html>
+          <head>
+            <script src="https://cdn.example.com/analytics.js"></script>
+            <script src="//cdn.example.com/protocol-relative.js"></script>
+            <script src="bar-abc123.js"></script>
+          </head>
+        </html>
+      HTML
+      assets = build_assets(name: "bar", asset_map: asset_map, index_html: index_html)
+
+      javascripts = assets.javascripts
+
+      expect(javascripts).to match_array([
+        "https://cdn.example.com/analytics.js",
+        "//cdn.example.com/protocol-relative.js",
+        "foo/bar-abc123.js",
+      ])
+    end
+
+    it "ignores scripts without a `src`" do
+      asset_map = {
+        "assets" => {
+          "bar.js" => "bar-abc123.js",
+        },
+        "prepend" => "foo/",
+      }
+      index_html = StringIO.new(<<~HTML)
+        <html>
+          <head>
+            <script>window.EmberENV = {};</script>
+            <script src="bar-abc123.js"></script>
+          </head>
+        </html>
+      HTML
+      assets = build_assets(name: "bar", asset_map: asset_map, index_html: index_html)
+
+      javascripts = assets.javascripts
+
+      expect(javascripts).to match_array(["foo/bar-abc123.js"])
+    end
+
     context "when the asset_map is empty" do
       it "raises a BuildError" do
         assets = build_assets(asset_map: {}, name: "bar", index_html: StringIO.new)
@@ -66,6 +115,33 @@
       ])
     end
 
+    it "passes stylesheets hosted outside the build through untouched" do
+      asset_map = {
+        "assets" => {
+          "bar.css" => "bar-abc123.css",
+        },
+        "prepend" => "foo/",
+      }
+      index_html = StringIO.new(<<~HTML)
+        <html>
+          <head>
+            <link rel="stylesheet" href="https://fonts.example.com/css?family=Bar"></link>
+            <link rel="stylesheet" href="//fonts.example.com/protocol-relative.css"></link>
+            <link rel="stylesheet" href="bar-abc123.css"></link>
+          </head>
+        </html>
+      HTML
+      assets = build_assets(name: "bar", asset_map: asset_map, index_html: index_html)
+
+      stylesheets = assets.stylesheets
+
+      expect(stylesheets).to match_array([
+        "https://fonts.example.com/css?family=Bar",
+        "//fonts.example.com/protocol-relative.css",
+        "foo/bar-abc123.css",
+      ])
+    end
+
     context "when the asset_map is empty" do
       it "raises a BuildError" do
         assets = build_assets(asset_map: {}, name: "bar", index_html: StringIO.new)