When you need to test your server you might find that gmail as one of the respectable smtp servers (and free) is a good solution.
Here’s how you can test from your box, connectivity to GMAIL
telnet smtp.gmail.com 587
Connected to smtp.gmail.com.
Escape character is ‘^]’.
220 smtp.gmail.com ESMTP m188sm6441342ioa.27 - gsmtp