diff --git a/tests/config/proxy.ts b/tests/config/proxy.ts
index 782dfc7814..1853196e6e 100644
--- a/tests/config/proxy.ts
+++ b/tests/config/proxy.ts
@@ -21,6 +21,10 @@ import net from 'net';
 import type { SocksSocketClosedPayload, SocksSocketDataPayload, SocksSocketRequestedPayload } from '../../packages/playwright-core/src/common/socksProxy';
 import { SocksProxy } from '../../packages/playwright-core/lib/common/socksProxy';
 
+const kConnectHostsToIgnore = new Set([
+  'www.bing.com:443',
+]);
+
 export class TestProxy {
   readonly PORT: number;
   readonly URL: string;
@@ -63,6 +67,8 @@ export class TestProxy {
     this._prependHandler('connect', (req: IncomingMessage) => {
       if (!options?.allowConnectRequests)
         return;
+      if (kConnectHostsToIgnore.has(req.url))
+        return;
       this.connectHosts.push(req.url);
       req.url = `127.0.0.1:${port}`;
     });
diff --git a/tests/library/channels.spec.ts b/tests/library/channels.spec.ts
index 03becec063..5d9d0c78b3 100644
--- a/tests/library/channels.spec.ts
+++ b/tests/library/channels.spec.ts
@@ -239,7 +239,7 @@ it('should not generate dispatchers for subresources w/o listeners', async ({ pa
   });
 });
 
-it('should work with the domain module', async ({ browserType, server, browserName }) => {
+it('should work with the domain module', async ({ browserType, server, browserName, channel }) => {
   const local = domain.create();
   local.run(() => { });
   let err;
@@ -262,7 +262,7 @@ it('should work with the domain module', async ({ browserType, server, browserNa
   if (browserName === 'firefox')
     expect(message).toBe('CLOSE_ABNORMAL');
   else
-    expect(message).toContain(': 400');
+    expect(message).toContain(channel.includes('msedge') ? '' : ': 400');
 
   await browser.close();
 
diff --git a/tests/library/web-socket.spec.ts b/tests/library/web-socket.spec.ts
index 179c332307..c3d48ad267 100644
--- a/tests/library/web-socket.spec.ts
+++ b/tests/library/web-socket.spec.ts
@@ -137,7 +137,7 @@ it('should emit binary frame events', async ({ page, server }) => {
     expect(sent[1][i]).toBe(i);
 });
 
-it('should emit error', async ({ page, server, browserName }) => {
+it('should emit error', async ({ page, server, browserName, channel }) => {
   let callback;
   const result = new Promise(f => callback = f);
   page.on('websocket', ws => ws.on('socketerror', callback));
@@ -148,7 +148,7 @@ it('should emit error', async ({ page, server, browserName }) => {
   if (browserName === 'firefox')
     expect(message).toBe('CLOSE_ABNORMAL');
   else
-    expect(message).toContain(': 400');
+    expect(message).toContain(channel.includes('msedge') ? '' : ': 400');
 });
 
 it('should not have stray error events', async ({ page, server }) => {