You are paying for the privilege to use highway and infrastructures in the United States and Canada. The more accurate that you are when stating your miles in each jurisdiction makes your payment for usage more accurate to each jurisdiction.
The grace period offered by Colorado allows the carrier the entire month following their expiration date to renew their registration. For example, if your expiration date is July 31, 2006, you have the month of August, 2006 to renew and pick up or receive by mail your permanent credentials. If a registration is not renewed, the registration expires on the expiration date with no grace period.
You should keep mileage records for the current registration and the prior three years on file. You may obtain these records from various sources. It is up to the carrier as to how they document miles traveled.