Ignatz, glad to see you around ;) Did you have a look at the Editor forum, already, btw?
You can either look for a provider for Backup MX, or rent a dedicated or virtual dedicated (VPS) server.
Usually this provider or server will accept mail and then attempt to send it to your home mail server (typically using ESMTP or more specifically, ETRN. In qmail, this could be accomplished by `echo domain.com:primarymailserverip > /var/qmail/control/smtproutes`
Some providers who offer explicit Backup services:
http://rollernet.us/mx.php (free)
http://www.dnsmadeeasy.com/s0306/prod/mailbk.html
http://www.dyndns.org/services/prici...x.html#mailhop
Greets