This works, of course, only if you have created the archive before disaster strikes. It will also only be as current as the date of your most recent archive.

The backup file for your iOS devices, as maintained via iTunes, contains the Contacts data. If you have not done a sync in iTunes since losing the data, you should be able to get it back via a restore. Fortunately, you don't need to do a complete restore--where you erase the iPhone's drive and restore everything, including the firmware. Instead, Control-click on the iOS device's name in the Devices section of iTunes. From the popup menu, select Restore from Backup.

Alternatively, I have seen discussions of how to use a utility, such as , to extract the needed data directly from the backup file and subsequently return it to your iPhone. The procedures typically are either overly complex or require a jailbroken device. I recommend avoiding the extraction approach, preferring Restore from Backup instead.

If one of your synced devices is an iPhone, go to Settings -> Mail, Contacts, Calendars and scroll down to the Import SIM Contacts button. Tap it. This will install the contacts contained on your SIM card to the Contacts app.

Unfortunately, this is not likely to be of much help, as the iPhone does not (as far as I know) transfer data from the Contacts app to the SIM card. However, if most of your contacts originally came from a prior import from a SIM card, this could bring them back.