Verizon blocks outgoing connections on port 25 (SMTP) unless you are connecting to their outgoing.verizon.net message exchange server. This server requires authentication with your Verzon username/password before it will accept your mail. For the purpose of this example, our Verizon username is jdoe, our Verizon password is YOURPASS, and were sending email from me@example.com to you@target.edu.

$ nc outgoing.verizon.net 25
220 vms173003pub.verizon.net -- Server ESMTP (...)
mail from: <jdoe@example.com>  
550 5.7.1 Authentication Required
quit
221 2.3.0 Bye received. Goodbye.

Because authenticating over an unencrypted connection is a Bad Idea™, I was looking for an encrypted way to send my outgoing email. Unfortunately, Verizon's exchange server does not support STARTTLS for encrypting connections to outgoing.verizon.net:25:

$ nc outgoing.verizon.net 25
220 vms173003pub.verizon.net -- Server ESMTP (...)
ehlo example.com
250-vms173003pub.verizon.net
250-8BITMIME
250-PIPELINING
250-CHUNKING
250-DSN
250-ENHANCEDSTATUSCODES
250-HELP
250-XLOOP E9B7EB199A9B52CF7D936A4DD3199D6F
250-AUTH DIGEST-MD5 PLAIN LOGIN CRAM-MD5
250-AUTH=LOGIN PLAIN
250-ETRN
250-NO-SOLICITING
250 SIZE 20971520
starttls
533 5.7.1 STARTTLS command is not enabled.
quit
221 2.3.0 Bye received. Goodbye.

Verizon recommends pre-STARTTLS approach of wrapping the whole SMTP connection in TLS (SMTPS), which it provides via outgoing.verizon.net:465:

$ python -c 'from base64 import *; print b64encode("\0jdoe@verizon.net\0YOURPASS")'
AGpkb2VAdmVyaXpvbi5uZXQAWU9VUlBBU1M=
$ openssl s_client -connect outgoing.verizon.net:465
...
220 vms173013pub.verizon.net -- Server ESMTP (...)
ehlo example.com
250-vms173013pub.verizon.net
250-8BITMIME
250-PIPELINING
250-CHUNKING
250-DSN
250-ENHANCEDSTATUSCODES
250-HELP
250-XLOOP 9380A5843FE933CF9BD037667F4C950D
250-AUTH DIGEST-MD5 PLAIN LOGIN CRAM-MD5
250-AUTH=LOGIN PLAIN
250-ETRN
250-NO-SOLICITING
250 SIZE 20971520
auth plain AGpkb2VAdmVyaXpvbi5uZXQAWU9VUlBBU1M
235 2.7.0 plain authentication successful.
mail from: <me@example.com>
250 2.5.0 Address Ok.
rcpt to: <you@target.edu>
250 2.1.5 you@target.edu OK.
data
354 Enter mail, end with a single ".".
From: Me <me@example.com>
To: You <you@target.edu>
Subject: testing

hello world 
.
250 2.5.0 Ok, envelope id 4BHMFEZ7PHSETMT6@vms173013.mailsrvcs.net
quit
221 2.3.0 Bye received. Goodbye.
closed

This works, but with the rise of STARTTLS, getting your local Postfix mail server to support SMTPS requires a bit of fancyness with stunnel. The stunnel workaround is not too complicated, but I also wanted to look into the submission protocol (port 587), which adapts SMTP (designed for message transfer) into a similar protocol for message submission. Unfortunately, Verizon does not support STARTTLS here either.

$ nc outgoing.verizon.net 587
220 vms173005.mailsrvcs.net -- Server ESMTP (...)
ehlo example.com
250-vms173005.mailsrvcs.net
250-8BITMIME
250-PIPELINING
250-CHUNKING
250-DSN
250-ENHANCEDSTATUSCODES
250-EXPN
250-HELP
250-XADR
250-XSTA
250-XCIR
250-XGEN
250-XLOOP DA941C5B31BE4B102BB69B809BC66C4A
250-AUTH DIGEST-MD5 PLAIN LOGIN CRAM-MD5
250-AUTH=LOGIN PLAIN
250-NO-SOLICITING
250 SIZE 20971520
starttls
533 5.7.1 STARTTLS command is not enabled.
quit
221 2.3.0 Bye received. Goodbye.

In conclusion, Verizon supports a number of email submission standards, but the only secure approach is to use the outdated SMTPS. See my Postfix post for details on configuring Postfix to use Verizon's server for outgoing mail.

There are a number of good SMTP authentication tutorials out there. I used John Simpson and Erwin Hoffmann's tutorials. For cleaner examples of my testing tools (nc and openssl s_client), see my simple servers post.