Any advice on how to humanely get rid of groundhogs?

[LunaSea]

10. Trap and relocate

Has been my method of dealing with such critters. Hav-a-hart traps are inexpensive and last for years.
http://www.havahart.com/

Study up on their behavior, it'll help figure out how best to bait and locate the trap as well as give you an idea of how far they need to be taken so they won't return.

I've used a few repellants for discouraging munchers away from the outdoor plants with fair results. Cayanne pepper works well as a general discouragement for all manner of rodentia.

I've tried to avoid using toxic chemistry for dealing with pests, but sometimes a strategic spray of ammonia will do the trick. Peeing into a spray bottle, and liberally dousing a perimeter around the area where they travel can also be effective.

Groundhogs are quite wily, you'll need to be patient and observant.
Good luck!