I set up my mx record to be "mail" with priority one. I am able to successfully ping firstname.lastname@example.org
I've followed this documentation: https://wiki.archlinux.org/index.php/sendmail
$ sendmail -vt < test-message.txt
The output looks like this (please note that I changed some of the stuff to hide my droplet name, domain name, and username. I've cap-locked those parts to make it obvious.
WARNING: local host name (DROPLET) is not qualified; see cf/README: WHO AM I?
TEST@EMAIL.COM... Connecting to [127.0.0.1] via relay...
220 MY-DOMAIN.COM ESMTP Sendmail 8.14.7/8.14.7; Mon, 23 Dec 2013 06:00:31 GMT
>>> EHLO camille
250-MY-DOMAIN.COM Hello localhost.localdomain [127.0.0.1], pleased to meet you
250 2.0.0 Verbose mode
>>> MAIL From: SIZE=111
050 ... Transient parse error -- message queued for future delivery
553 5.1.8 ... Domain of sender address MY-LOGIN@MY-DROPLET does not exist
.../dead.letter... Saved message in .../dead.letter
Closing connection to [127.0.0.1]
221 2.0.0 MY-DOMAIN.COM closing connection
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