iPhone cannot verify server identity

If you're able to receive but not send mail, I can confirm that this is all related to a bug in the SMTP server settings stored on the device. Someone else mentioned a version of this solution earlier, but here's a step-by-step guide to how I finally cleared it up after a day of dangerously high blood pressure:

If you have more than one mail account, skip to step 2.

1. Only applicable if you have one mail account on your phone: Create a bogus mail account with fake settings. Just get it to be saved as a legit-looking account, and you should be OK.
2. Delete the problematic account.
3. In any other mail account, find where all your SMTP servers are listed (Account > SMTP).
4. The one from the problematic account should still be there. Tap on it to get the details, and hit Delete Server.
5. Make sure you don't have multiple listings for it. If you do, delete those, too.
6. Re-add the account you deleted. You should finally get the full Cannot Verify Server Identity dialog with Continue, Details, and Cancel.
7. Assuming you need to trust the certificate, hit Details. You should see the Trust option. Tap it!
8. You may need to repeat step 7 to cover both incoming and outgoing servers.
9. If you created a bogus account in step 1, be sure to delete it or Mail will get stuck on trying to get it to work.

This worked for me. I hope it works for you if you have the same problem I did.