There are online services that will let you test the server while specifying TLS versions -- meaning you can say "connect to this server using only TLSv1.1".

CheckTLS.com tests TLS on mail servers but you can force it to test HTTPS (443). From their //email/testTo (TestReceiver) test, set the Target to the host you want to test, and under Advanced Options set the mx port to 443, turn on Direct TLS, and put TLSv1_1 or TLSv1_2 in the TLS Version field.