diff --git a/integration/mdc-migration/golden/src/broken.css b/integration/mdc-migration/golden/src/broken.css
new file mode 100644
index 000000000000..0fd1c6dde9ca
--- /dev/null
+++ b/integration/mdc-migration/golden/src/broken.css
@@ -0,0 +1,5 @@
+/* Does not compile (missing semicolons) */
+.mat-button {
+  width: 100
+  height: 100
+}
diff --git a/integration/mdc-migration/golden/src/dont-migrate-me.css.skip b/integration/mdc-migration/golden/src/dont-migrate-me.css.skip
new file mode 100644
index 000000000000..fe4cfdd8c542
--- /dev/null
+++ b/integration/mdc-migration/golden/src/dont-migrate-me.css.skip
@@ -0,0 +1,4 @@
+/* Should not be migrated (filename is not .css or .scss) */
+.mat-button {
+  width: 100px;
+}
diff --git a/integration/mdc-migration/sample-project/src/broken.css b/integration/mdc-migration/sample-project/src/broken.css
new file mode 100644
index 000000000000..0fd1c6dde9ca
--- /dev/null
+++ b/integration/mdc-migration/sample-project/src/broken.css
@@ -0,0 +1,5 @@
+/* Does not compile (missing semicolons) */
+.mat-button {
+  width: 100
+  height: 100
+}
diff --git a/integration/mdc-migration/sample-project/src/dont-migrate-me.css.skip b/integration/mdc-migration/sample-project/src/dont-migrate-me.css.skip
new file mode 100644
index 000000000000..fe4cfdd8c542
--- /dev/null
+++ b/integration/mdc-migration/sample-project/src/dont-migrate-me.css.skip
@@ -0,0 +1,4 @@
+/* Should not be migrated (filename is not .css or .scss) */
+.mat-button {
+  width: 100px;
+}
diff --git a/src/cdk/schematics/ng-update/find-stylesheets.ts b/src/cdk/schematics/ng-update/find-stylesheets.ts
index 13f7f651fe09..8702835f2f5d 100644
--- a/src/cdk/schematics/ng-update/find-stylesheets.ts
+++ b/src/cdk/schematics/ng-update/find-stylesheets.ts
@@ -10,7 +10,7 @@ import {join, Path} from '@angular-devkit/core';
 import {Tree} from '@angular-devkit/schematics';
 
 /** Regular expression that matches stylesheet paths */
-const STYLESHEET_REGEX = /.*\.(css|scss)/;
+const STYLESHEET_REGEX = /.*\.(css|scss)$/;
 
 /**
  * Finds stylesheets in the given directory from within the specified tree.
diff --git a/src/material/schematics/ng-generate/mdc-migration/BUILD.bazel b/src/material/schematics/ng-generate/mdc-migration/BUILD.bazel
index beed7ee26cd0..581c49f575cc 100644
--- a/src/material/schematics/ng-generate/mdc-migration/BUILD.bazel
+++ b/src/material/schematics/ng-generate/mdc-migration/BUILD.bazel
@@ -91,6 +91,7 @@ jasmine_node_test(
         "//src/material/schematics:collection_assets",
         "//src/material/schematics:ng_generate_assets",
     ],
+    shard_count = 10,
     deps = [
         ":unit_tests_bundle",
         # Runtime dependencies needed by the test and actual migration sources. These need
diff --git a/src/material/schematics/ng-generate/mdc-migration/rules/theming-styles.ts b/src/material/schematics/ng-generate/mdc-migration/rules/theming-styles.ts
index 65398700d5b7..74054ddba117 100644
--- a/src/material/schematics/ng-generate/mdc-migration/rules/theming-styles.ts
+++ b/src/material/schematics/ng-generate/mdc-migration/rules/theming-styles.ts
@@ -22,10 +22,10 @@ export class ThemingStylesMigration extends Migration<ComponentMigrator[], Schem
     this.fileSystem
       .edit(stylesheet.filePath)
       .remove(stylesheet.start, stylesheet.content.length)
-      .insertRight(stylesheet.start, this.migrate(stylesheet.content));
+      .insertRight(stylesheet.start, this.migrate(stylesheet.content, stylesheet.filePath));
   }
 
-  migrate(styles: string): string {
+  migrate(styles: string, filename: string): string {
     const processor = new postcss.Processor([
       {
         postcssPlugin: 'theming-styles-migration-plugin',
@@ -37,7 +37,13 @@ export class ThemingStylesMigration extends Migration<ComponentMigrator[], Schem
       },
     ]);
 
-    return processor.process(styles, {syntax: scss}).toString();
+    try {
+      return processor.process(styles, {syntax: scss}).toString();
+    } catch (e) {
+      this.context.logger.error(`${e}`);
+      this.context.logger.warn(`Failed to process stylesheet: ${filename} (see error above).`);
+      return styles;
+    }
   }
 
   atUseHandler(atRule: postcss.AtRule) {
diff --git a/src/material/schematics/ng-generate/mdc-migration/rules/ts-migration/runtime-migration.ts b/src/material/schematics/ng-generate/mdc-migration/rules/ts-migration/runtime-migration.ts
index 6d813e802185..cacbb509e896 100644
--- a/src/material/schematics/ng-generate/mdc-migration/rules/ts-migration/runtime-migration.ts
+++ b/src/material/schematics/ng-generate/mdc-migration/rules/ts-migration/runtime-migration.ts
@@ -134,7 +134,7 @@ export class RuntimeCodeMigration extends Migration<ComponentMigrator[], Schemat
     node: ts.StringLiteralLike | ts.Identifier,
     migration: TemplateMigration | ThemingStylesMigration,
   ) {
-    let migratedText = migration.migrate(node.text);
+    let migratedText = migration.migrate(node.text, node.getSourceFile().fileName);
     let migratedTextLines = migratedText.split('\n');
 
     // Update quotes based on if its multiline or not to avoid compilation errors
diff --git a/src/material/schematics/ng-update/migrations/legacy-components-v15/index.ts b/src/material/schematics/ng-update/migrations/legacy-components-v15/index.ts
index 700df477436b..a9c532df47d8 100644
--- a/src/material/schematics/ng-update/migrations/legacy-components-v15/index.ts
+++ b/src/material/schematics/ng-update/migrations/legacy-components-v15/index.ts
@@ -37,7 +37,12 @@ export class LegacyComponentsMigration extends Migration<null> {
         RootExit: root => this._handleRootNode(root, stylesheet.filePath, namespace),
       },
     ]);
-    processor.process(stylesheet.content, {syntax: scss}).sync();
+    try {
+      processor.process(stylesheet.content, {syntax: scss}).sync();
+    } catch (e) {
+      this.logger.error(`${e}`);
+      this.logger.warn(`Failed to process stylesheet: ${stylesheet.filePath} (see error above).`);
+    }
   }
 
   /** Returns the namespace of the given at-rule if it is importing from @angular/material. */