At least twice a week some user will say they’ve emailed someone and they’re not get a response back from them. The first thing I ask my user is if they’ve received an NDR (non delivery report) in their inbox. If they say no then I jump on my mail server and run a simple telnet command to the destination domain mail server (which you can easily get from mxtoolbox.com):
telnet domain-in-question-smtp-server.com/net/org/etc 25 (press enter)
If your email server is NOT blocked then you’ll usually receive a 220 message (which is good). Any other message most likely means their mail service is blocking you.