diff --git a/.github/workflows/cf_unit_tests.yml b/.github/workflows/cf_unit_tests.yml
new file mode 100644
index 000000000..0392746b6
--- /dev/null
+++ b/.github/workflows/cf_unit_tests.yml
@@ -0,0 +1,33 @@
+name: "Playwright for Cloudflare - Unit Tests"
+
+on:
+  pull_request:
+    paths:
+      - "packages/playwright-cloudflare/src/**"
+      - "packages/playwright-cloudflare/tests/**"
+      - ".github/workflows/cf_unit_tests.yml"
+  push:
+    branches: [main]
+    paths:
+      - "packages/playwright-cloudflare/src/**"
+      - "packages/playwright-cloudflare/tests/**"
+      - ".github/workflows/cf_unit_tests.yml"
+
+permissions:
+  contents: read
+
+jobs:
+  unit-tests:
+    runs-on: ubuntu-latest
+    defaults:
+      run:
+        working-directory: packages/playwright-cloudflare/tests
+    steps:
+      - uses: actions/checkout@v4
+      - uses: actions/setup-node@v4
+        with:
+          node-version: "20.x"
+          cache: npm
+          cache-dependency-path: packages/playwright-cloudflare/tests/package-lock.json
+      - run: npm ci
+      - run: npm run test:unit
diff --git a/packages/playwright-cloudflare/src/cloudflare/webSocketTransport.ts b/packages/playwright-cloudflare/src/cloudflare/webSocketTransport.ts
index 86c4697df..b530a9a22 100644
--- a/packages/playwright-cloudflare/src/cloudflare/webSocketTransport.ts
+++ b/packages/playwright-cloudflare/src/cloudflare/webSocketTransport.ts
@@ -7,6 +7,7 @@ export const transportZone = new AsyncLocalStorage<WebSocketTransport>();
 
 export class WebSocketTransport implements ConnectionTransport {
   private _ws: WebSocket;
+  private _closing = false;
   onmessage?: (message: ProtocolResponse) => void;
   onclose?: () => void;
   readonly sessionId: string | undefined;
@@ -26,19 +27,26 @@ export class WebSocketTransport implements ConnectionTransport {
       this.onmessage?.(JSON.parse(event.data) as ProtocolResponse);
     });
     this._ws.addEventListener('close', () => {
+      this._closing = true;
       this.onclose?.();
     });
     this._ws.addEventListener('error', e => {
+      if (this._closing)
+        return;
       // eslint-disable-next-line no-console
       console.error(`Websocket error${sessionId ? `: SessionID: ${sessionId}` : ''}`, e);
     });
   }
 
   send(message: ProtocolRequest): void {
+    // Browser Run can raise an error event while completing a requested shutdown.
+    if (message.method === 'Browser.close')
+      this._closing = true;
     this._ws.send(JSON.stringify(message));
   }
 
   close(): void {
+    this._closing = true;
     this._ws.close();
     this.onclose?.();
   }
diff --git a/packages/playwright-cloudflare/tests/package.json b/packages/playwright-cloudflare/tests/package.json
index 2d3ad3116..7aa11143c 100644
--- a/packages/playwright-cloudflare/tests/package.json
+++ b/packages/playwright-cloudflare/tests/package.json
@@ -7,6 +7,7 @@
   "description": "",
   "types": "./test-d/index.d.ts",
   "scripts": {
+    "test:unit": "playwright test --config=unit/playwright.config.ts",
     "test-types": "tsd"
   },
   "devDependencies": {
diff --git a/packages/playwright-cloudflare/tests/unit/playwright.config.ts b/packages/playwright-cloudflare/tests/unit/playwright.config.ts
new file mode 100644
index 000000000..411087cf2
--- /dev/null
+++ b/packages/playwright-cloudflare/tests/unit/playwright.config.ts
@@ -0,0 +1,6 @@
+import { defineConfig } from '@playwright/test';
+
+export default defineConfig({
+  testDir: '.',
+  workers: 1,
+});
diff --git a/packages/playwright-cloudflare/tests/unit/webSocketTransport.spec.ts b/packages/playwright-cloudflare/tests/unit/webSocketTransport.spec.ts
new file mode 100644
index 000000000..9891dea36
--- /dev/null
+++ b/packages/playwright-cloudflare/tests/unit/webSocketTransport.spec.ts
@@ -0,0 +1,89 @@
+import { test as base, expect } from '@playwright/test';
+
+import { WebSocketTransport } from '../../src/cloudflare/webSocketTransport';
+
+const test = base.extend<{ errors: unknown[][] }>({
+  errors: async ({}, use) => {
+    const errors: unknown[][] = [];
+    // eslint-disable-next-line no-console
+    const original = console.error;
+    // eslint-disable-next-line no-console
+    console.error = (...args: unknown[]) => errors.push(args);
+    try {
+      await use(errors);
+    } finally {
+      // eslint-disable-next-line no-console
+      console.error = original;
+    }
+  },
+});
+
+class MockWebSocket extends EventTarget {
+  sent: string[] = [];
+
+  send(message: string) {
+    this.sent.push(message);
+    this.dispatchEvent(new Event('error'));
+  }
+
+  close() {
+    this.dispatchEvent(new Event('error'));
+  }
+}
+
+test('reports errors while the browser session is active', async ({ errors }) => {
+  const ws = new MockWebSocket();
+  new WebSocketTransport(ws as unknown as WebSocket, 'session-id');
+  const error = new Event('error');
+
+  ws.dispatchEvent(error);
+
+  expect(errors).toEqual([['Websocket error: SessionID: session-id', error]]);
+});
+
+test('does not report errors raised while closing the transport', async ({ errors }) => {
+  const ws = new MockWebSocket();
+  const transport = new WebSocketTransport(ws as unknown as WebSocket, undefined);
+  let closed = false;
+  transport.onclose = () => closed = true;
+
+  transport.close();
+
+  expect(errors.length).toBe(0);
+  expect(closed).toBe(true);
+});
+
+test('does not report errors after sending Browser.close', async ({ errors }) => {
+  const ws = new MockWebSocket();
+  const transport = new WebSocketTransport(ws as unknown as WebSocket, 'session-id');
+  const message = { id: -9999, method: 'Browser.close', params: {} };
+
+  transport.send(message);
+  ws.dispatchEvent(new Event('error'));
+
+  expect(errors.length).toBe(0);
+  expect(ws.sent).toEqual([JSON.stringify(message)]);
+});
+
+test('reports errors when sending other protocol commands', async ({ errors }) => {
+  const ws = new MockWebSocket();
+  const transport = new WebSocketTransport(ws as unknown as WebSocket, undefined);
+
+  transport.send({ id: 1, method: 'Browser.getVersion', params: {} });
+
+  expect(errors).toHaveLength(1);
+  expect(errors[0][0]).toBe('Websocket error');
+});
+
+test('does not report errors after the websocket closes', async ({ errors }) => {
+  const ws = new MockWebSocket();
+  const transport = new WebSocketTransport(ws as unknown as WebSocket, 'session-id');
+  let closed = false;
+  transport.onclose = () => closed = true;
+
+  ws.dispatchEvent(new Event('close'));
+  ws.dispatchEvent(new Event('error'));
+
+  expect(errors.length).toBe(0);
+  expect(closed).toBe(true);
+});