diff --git a/Lib/test/support/threading_helper.py b/Lib/test/support/threading_helper.py
index 0632577cdb..18c88cb594 100644
--- a/Lib/test/support/threading_helper.py
+++ b/Lib/test/support/threading_helper.py
@@ -183,12 +183,13 @@ class catch_threading_exception:
         # (to avoid reference cycles)
     """
 
-    def __init__(self):
+    def __init__(self, cleanup=None):
         self.exc_type = None
         self.exc_value = None
         self.exc_traceback = None
         self.thread = None
         self._old_hook = None
+        self.cleanup = cleanup
 
     def _hook(self, args):
         self.exc_type = args.exc_type
@@ -203,6 +204,8 @@ class catch_threading_exception:
 
     def __exit__(self, *exc_info):
         threading.excepthook = self._old_hook
+        if self.cleanup is not None:
+            self.cleanup(self.exc_type, self.exc_value, self.exc_traceback, self.thread)
         del self.exc_type
         del self.exc_value
         del self.exc_traceback
diff --git a/Lib/test/test_ssl.py b/Lib/test/test_ssl.py
index ecb6049a67..b6595bd11b 100644
--- a/Lib/test/test_ssl.py
+++ b/Lib/test/test_ssl.py
@@ -4430,7 +4430,12 @@ class TestPostHandshakeAuth(unittest.TestCase):
 
         # Ignore expected SSLError in ConnectionHandler of ThreadedEchoServer
         # (it is only raised sometimes on Windows)
-        with threading_helper.catch_threading_exception() as cm:
+        # If this is raised we will manually cleanup to avoid a
+        # ResourceWarning
+        def thread_cleanup(exc_type, exc_value, exc_traceback, thread):
+            if exc_type == ssl.SSLError:
+                thread.sslconn.close()
+        with threading_helper.catch_threading_exception(thread_cleanup) as cm:
             server = ThreadedEchoServer(context=server_context, chatty=False)
             with server:
                 with client_context.wrap_socket(socket.socket(),
@@ -4447,6 +4452,17 @@ class TestPostHandshakeAuth(unittest.TestCase):
                             'tlsv13 alert certificate required'):
                         s.recv(1024)
 
+                    # If ConnectionHandler did raise an SSLError manually
+                    # close the connection to avoid a ResourceWarning
+                    # Note: there is a race condition where
+                    # the details of the exception in the thread may not be
+                    # populated in cm before __exit__
+                    # is called. As a very naive approach add a sleep to avoid
+                    # this
+                    time.sleep(1)
+                    if cm.exc_type == ssl.SSLError:
+                        cm.thread.sslconn.close()
+
     def test_pha_optional(self):
         if support.verbose:
             sys.stdout.write("\n")