For what they are, Garmin bike computers have excellent battery life (generally ~10hrs). This capacity is enough to easily navigate and record 100-150 mile rides. If you try to go much further (especially if recording *and* navigating a route) you may find your recording (and your proof) cut short.
Garmin devices will accept a charge while operating normally so the answer is to get an external USB battery pack and plug it in.
Almost any USB charger will do but how you affix it to your bike will depend on the type you get, and the model of your Garmin. For example: Garmin 705′s have the USB port on the BOTTOM of the device which may be difficult to access if you have a wide stem. You’ll also want to check the HEIGHT of your computer if you have a ’500 or ’800 to make sure that the SIDE facing USB ports clear your stem cap so the USB plug will not be obstructed.
From what I’ve read, charging your computer at rest stops will not give you much of a boost. If possible, it is best to continuously feed the Garmin power until your external battery dies, then unplug and continue on with the internal. Here are a few pictures showing a Duracell Instant USB Charger attached to a Garmin Edge 800.