You have two basic options --

1. Run an SMTP server locally.
2. Deliver directly to the recipient's mail server

If you're running a server locally, it doesn't have to listen to on a port. You can configure some mail programs (sendmail being the standard, but I've also done it with postfix), so they're running as a daemon, and accept local delivery, and will handle the processing. (including requeuing on failed delivery attempts). I typically do this on any desktop, as you can have times when a cron job fails delivery, and it just gets left in the mailqueue.

If you attempt to handle the delivery directly, you can use Net::SMTP to connect to the server and drop off the mail. However, you'll need to determine the correct MX server to drop off the mail. (see Net::DNS). Remember, however, that you'll be responsible for any requeuing that might be necessary.

Please also be aware that many sites are using multiple layers of spam filtering, both on the inbound and outbound. Your network may not allow port 25 connections out, and if you're connecting through an ISP, your netblock may be flagged as a dialup (or similar, non-fixed) connection, and the message could be dropped on receipt, without a response.