(Based on a post to the ProviderTalk mailing list 18 Sept 2003.)
% dig mx <maindomain.com>where <maindomain.com> is what appears after the "@" sign in e-mail addresses.
% telnet <backup.server.com> 587
[Server responds with information about the server]
ehlo vmailpros.com
[Server responds that it is pleased to meet you,
and suggests possible commands]
mail from: <benlanford@gmail.com>
[Server responds that the sender is OK]
rcpt to: <realuser@maindomain.com>
[Server responds that the recipient is OK]
data
[Server says to enter mail, ending with "."
on a line by itself]
This is a test message
. {The dot at left should appear all by itself}
[Server should respond that the message is accepted]
quit
If the above steps work as described, then your backup server is set up correctly.