I have a PHP script that sends out critical e-mails that needs to reach its destination. I know how to check whether the e-mail sent successfully, the only issue is knowing
If it's internal, send the email, but don't put the content of the message in the email. Provide a link to a web site and but an identifier in the url so that you can tie the page-view to the email.
You can still do that if it's external, as long as the people on the other end are cooperative.
You can also set up a vanilla account on the destination mail system and check that. If you get the email at that account, odds are the system is not set to filter it out.
You can also ask the admins of the receiving system to give you a bounce-back on well-received emails (you know, script that curls your acknowledgment web page), but that would require a lot of cooperation. Although at that point, it might be easier to deliver the message through a web service.