[Pushing up from comments]

Two options:

  • Batch mode from text-based browsers such as links/lynx/w3m
  • Use openssl s_client as noted here: Connecting to HTTPS with netcat (nc)

If you can ssh into the server, I recommend this:

  1. Think of a random port, like 5555 that you will use on your local machine.
  2. Run ssh -L 5555:remote_server:443 username@aix_server
  3. Point your browser to https://localhost:5555/

Your browser will report an error that the certificate is not for localhost, but for the remote_server, but at least you would have proved that the connectivity works. You could also use openssl s_client -connect localhost:5555, as noted on other answers to verify more in detail the encrypted communication.

Good luck!