Contact reminders are properties of the contacts. They are not separate data items that you can back up. Back up your contacts (see http://www.slipstick.com/config/backup.htm) and you'll back up the reminders.
Contacts do not support recurring reminders. You will need to set each reminder every time you want to use it.
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Sue Mosher, Outlook MVP
Author of Configuring Microsoft Outlook 2003
and Microsoft Outlook Programming - Jumpstart for
Administrators, Power Users, and Developers