Most people I know use a telnet to port 25 when they need to test SMTP to a mail server, be it with Exim, sendmail or any other. I did that for years, and it is of course quite sufficient and rather effective for basic connectivity testing, but it gets inefficient quickly. Testing SSL or TLS cannot be done with telnet of course, but OpenSSL’s s_client can be used for that.

If you need to do more, such as testing TLS or even SMTP authentication (SMTP AUTH), I strongly recommend John Jetmore’s swaks. Swaks, the SMTP transaction tester, is a Perl program which requires a few modules for its advanced features but performs basic tasks without them. Do read the documentation (the program is its own manual: perldoc swaks) for a list of all its features.