In order to do this you must define two options in your /etc/mail/sendmail.mc file:
In the above options, "hostname" is the hostname of the backup mail server. After you have added those options, you need to execute the commands:
make -C /etc/mail
service sendmail restart
These commands will rebuild the Sendmail macro configuration file for m4 and then restart the Sendmail service, respectively.
Note: This configuration should also work if the internal backup server is a Microsoft Exchange mail server