The following isn't necessarily the "proper way", but it's something that came to mind. I find it useful when debugging Perl CGI stuff for https:// servers to use `stunnel`. It's like telnet but uses SSL protocol. Example:

$ stunnel -cr foo.com:443
GET /cgi-bin/store.pl HTTP/1.0

HTTP/1.1 302 Moved
Date: Wed, 21 Nov 2001 21:32:06 GMT
Server: Apache/1.3.22 (Unix) mod_ssl/2.8.5 OpenSSL/0.9.6b
location: /store/index.html
Connection: close
Content-Type: text/plain
[download]

There I used it like a telnet client. You can also pipe stuff to it (actually, you can pipe stuff to telnet, too). I'm not sure offhand how to get LWP::Simple to use stunnel, though.