diff --git a/tests/net_inet/asyncio_tls_open_connection_readline.py b/tests/net_inet/asyncio_tls_open_connection_readline.py
index a0df88be4a..492b85a5db 100644
--- a/tests/net_inet/asyncio_tls_open_connection_readline.py
+++ b/tests/net_inet/asyncio_tls_open_connection_readline.py
@@ -2,6 +2,10 @@ import ssl
 import os
 import asyncio
 
+if not hasattr(ssl, "CERT_REQUIRED"):
+    print("SKIP")
+    raise SystemExit
+
 # This certificate was obtained from micropython.org using openssl:
 # $ openssl s_client -showcerts -connect micropython.org:443 </dev/null 2>/dev/null
 # The certificate is from Let's Encrypt:
diff --git a/tests/net_inet/ssl_cert.py b/tests/net_inet/ssl_cert.py
index 7bb270d5fd..4f065c5657 100644
--- a/tests/net_inet/ssl_cert.py
+++ b/tests/net_inet/ssl_cert.py
@@ -1,6 +1,9 @@
 import socket
 import ssl
 
+if not hasattr(ssl, "CERT_REQUIRED"):
+    print("SKIP")
+    raise SystemExit
 
 # This certificate was obtained from micropython.org using openssl:
 # $ openssl s_client -showcerts -connect micropython.org:443 </dev/null 2>/dev/null
diff --git a/tests/net_inet/ssl_errors.py b/tests/net_inet/ssl_errors.py
index bc4e5910bc..c23f736b09 100644
--- a/tests/net_inet/ssl_errors.py
+++ b/tests/net_inet/ssl_errors.py
@@ -3,6 +3,10 @@
 
 import sys, errno, select, socket, ssl
 
+if not hasattr(ssl, "CERT_REQUIRED"):
+    print("SKIP")
+    raise SystemExit
+
 
 def test(addr, hostname, block=True):
     print("---", hostname)
diff --git a/tests/net_inet/test_sslcontext_client.py b/tests/net_inet/test_sslcontext_client.py
index 77f68da496..bc06dc3c58 100644
--- a/tests/net_inet/test_sslcontext_client.py
+++ b/tests/net_inet/test_sslcontext_client.py
@@ -2,6 +2,10 @@ import os
 import socket
 import ssl
 
+if not hasattr(ssl, "CERT_REQUIRED"):
+    print("SKIP")
+    raise SystemExit
+
 # This certificate was obtained from micropython.org using openssl:
 # $ openssl s_client -showcerts -connect micropython.org:443 </dev/null 2>/dev/null
 # The certificate is from Let's Encrypt:
diff --git a/tests/net_inet/test_tls_nonblock.py b/tests/net_inet/test_tls_nonblock.py
index 60af858b1f..3f9a61413f 100644
--- a/tests/net_inet/test_tls_nonblock.py
+++ b/tests/net_inet/test_tls_nonblock.py
@@ -1,5 +1,12 @@
 import socket, ssl, errno, sys, time, select
 
+# Although this test doesn't need ssl.CERT_REQUIRED, it does require the ssl module
+# to support modern ciphers.  So exclude the test on axTLS which doesn't have
+# CERT_REQUIRED.
+if not hasattr(ssl, "CERT_REQUIRED"):
+    print("SKIP")
+    raise SystemExit
+
 
 def test_one(site, opts):
     ai = socket.getaddrinfo(site, 443, socket.AF_INET)