diff --git a/Lib/test/test_imaplib.py b/Lib/test/test_imaplib.py
index fac6b570812..9df37b1de58 100644
--- a/Lib/test/test_imaplib.py
+++ b/Lib/test/test_imaplib.py
@@ -966,6 +966,9 @@ class RemoteIMAP_SSLTest(RemoteIMAPTest):
             _server = self.imap_class(self.host, self.port)
             self.check_logincapa(_server)
 
+    @unittest.skipIf(True,
+                     "bpo-30175: FIXME: cyrus.andrew.cmu.edu doesn't accept "
+                     "our randomly generated client x509 certificate anymore")
     def test_logincapa_with_client_certfile(self):
         with transient_internet(self.host):
             with support.check_warnings(('', DeprecationWarning)):
@@ -973,6 +976,9 @@ class RemoteIMAP_SSLTest(RemoteIMAPTest):
                                           certfile=CERTFILE)
                 self.check_logincapa(_server)
 
+    @unittest.skipIf(True,
+                     "bpo-30175: FIXME: cyrus.andrew.cmu.edu doesn't accept "
+                     "our randomly generated client x509 certificate anymore")
     def test_logincapa_with_client_ssl_context(self):
         with transient_internet(self.host):
             _server = self.imap_class(
diff --git a/Lib/test/test_nntplib.py b/Lib/test/test_nntplib.py
index c46ded11866..3e84f3429ee 100644
--- a/Lib/test/test_nntplib.py
+++ b/Lib/test/test_nntplib.py
@@ -286,7 +286,12 @@ class NetworkedNNTPTests(NetworkedNNTPTestsMixin, unittest.TestCase):
     def setUpClass(cls):
         support.requires("network")
         with support.transient_internet(cls.NNTP_HOST):
-            cls.server = cls.NNTP_CLASS(cls.NNTP_HOST, timeout=TIMEOUT, usenetrc=False)
+            try:
+                cls.server = cls.NNTP_CLASS(cls.NNTP_HOST, timeout=TIMEOUT,
+                                            usenetrc=False)
+            except EOFError:
+                raise unittest.SkipTest(f"{cls} got EOF error on connecting "
+                                        f"to {cls.NNTP_HOST!r}")
 
     @classmethod
     def tearDownClass(cls):