I had great success with SOAP::Lite. It was very easy to use and enabled me to concentrate on my real problem. I had a working system in under a day that moved hundreds of thousands of records securely over HTTPS.

SOAP::Lite uses LWP and gets the benefit of secure connections if you have the right modules installed. I used Crypt::SSLea, but I think there is another one as well. They both use OpenSSL.