When web hosts lock down their firewalls, they often close commonly used outgoing SMTP ports. Most everyone is used to port 25 being blocked, but my web host was also blocking 465 and 587 which are the common ports for sending SMTP traffic over SSL and TLS connections.
Of course, when you get the first level support guys trying to mess with the firewall, they are rarely successful. It is handy to have a command you and they can run to check their work.
Here are the openssl commands for checking the connections. These connect to google's gmail servers.
The first command connects on port 465 is typically used for SMTP traffic over SSL. You can test different versions of SSL with the -ssl2 and -ssl3 options. There is nothing email specific about the command. A small variation can be used to check https connections (HTTP over SSL)