diff --git a/CHANGES.rst b/CHANGES.rst
index d39895a9f29..8de0fd00ebb 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -90,6 +90,9 @@ Bugs fixed
   Patch by Bénédikt Tran.
 * #12008: Fix case-sensitive lookup of ``std:label`` names in intersphinx inventory.
   Patch by Michael Goerz.
+* #12038: Resolve ``linkcheck`` unit test timeouts on Windows by adding a readiness
+  check to the test HTTP(S) server setup code.
+  Patch by James Addison.
 
 Testing
 -------
diff --git a/tests/utils.py b/tests/utils.py
index 32636b7936c..c82c449dbde 100644
--- a/tests/utils.py
+++ b/tests/utils.py
@@ -1,6 +1,7 @@
 import contextlib
 import http.server
 import pathlib
+import socket
 import threading
 from ssl import PROTOCOL_TLS_SERVER, SSLContext
 
@@ -15,11 +16,15 @@
 # File lock for tests
 LOCK_PATH = str(TESTS_ROOT / 'test-server.lock')
 
+HOST_NAME = "localhost"
+HOST_PORT = 7777
+ADDRESS = (HOST_NAME, HOST_PORT)
+
 
 class HttpServerThread(threading.Thread):
     def __init__(self, handler, *args, **kwargs):
         super().__init__(*args, **kwargs)
-        self.server = http.server.ThreadingHTTPServer(("localhost", 7777), handler)
+        self.server = http.server.ThreadingHTTPServer(ADDRESS, handler)
 
     def run(self):
         self.server.serve_forever(poll_interval=0.001)
@@ -45,7 +50,8 @@ def server(handler):
             server_thread = thread_class(handler, daemon=True)
             server_thread.start()
             try:
-                yield server_thread
+                socket.create_connection(ADDRESS, timeout=0.5).close()  # Attempt connection.
+                yield server_thread  # Connection has been confirmed possible; proceed.
             finally:
                 server_thread.terminate()
     return contextlib.contextmanager(server)