With a sharp, pointed knife, make one or two slits (depending on size of ducks) in duck breasts. Insert one or two slivers of garlic in each slit. Rub outside and inside cavities of ducks with a liberal amount of salt and cayenne. Place ducks, breast-side down, in a large deep bowl.
In another bowl, combine celery, bell pepper, and onion, and season with salt and cayenne. Stuff half of mixture in duck cavities and place remaining half around ducks in bowl. Pour dry sherry over ducks.
Cover and refrigerate for at least 4 hours, turning ducks once or twice in marinade. Remove ducks from refrigerator, drain, and reserve marinade.