I had a need recently to test an HTTPS connection from one remote location to another. Not having a graphical browser available with which to test, I had to use a text-based tool. 'lynx' is a text-based browser that was available on the client end, but it does not support SSL. 'elinks' is lynx-like program, which DOES support SSL, but was not installed on the client side.
Another option is to use 'openssl'. Although it's not fancy, it will suffice to test an SSL connection. For example,
# openssl s_client -connect google.com:443
which should produce output like:
depth=1 C = US, O = Google Inc, CN = Google Internet Authority
verify error:num=20:unable to get local issuer certificate
0 s:/C=US/ST=California/L=Mountain View/O=Google Inc/CN=*.google.com
i:/C=US/O=Google Inc/CN=Google Internet Authority
1 s:/C=US/O=Google Inc/CN=Google Internet Authority
i:/C=US/O=Equifax/OU=Equifax Secure Certificate Authority
Once connected, it's possible to make simple requests by entering a GET command, such as:
Enter Q to quit.