Take a look at your email server logs. You should see a message indicating that the client host has been blocked by a blacklist and that your IP has been banned. When you send the email you should also get a non delivery report back from Microsoft.
If you are blocked by the blacklist you can email email@example.com and include your IP address that emails are being sent from and they can start the process and tell you what you need to do to be delisted from the blacklist.
If you haven't been blocked take a do a DNS dig and check what the MX records are for the specific domains you are trying to send emails to and do a trace route as there could be an issue before the mail servers, unlikely but still possible.