Step 1: Obtain collector insurance for your vehicle(s)
Step 2: Have your insurance agent fax a copy of your declaration page to AZ DMV at this number: 602-712-3288. This will serve to notify DMV that your vehicle is eligible to waive emissions testing, due to mileage restrictions placed upon it by your insurance company.
Step 3: sign on to the DMV website at servicearizona.com (I waited 24 hours after submittal of fax)
Step 4: Follow the steps for vehicle registration renewal.

For my '79 Capri, the registration costs are as follows:
1-year: $19.75
2-year: $31.25
5-year: $65.75. That's $13 per year for registration! Not bad.