There are quite a few posts about locking your hen into a small cage with a wire bottom for 3 - 5 days until the broodiness stops. My "broody Ethel" is going on three weeks of brooding, but is still eating and drinking. I take her out of the coop a couple of times a day and make sure she is okay, and watch her eat and drink. She will run around for 30 minutes or so, and then head right back to the nest. Although she has nothing to hatch, she does let the other hens in to lay eggs and seems to take some kind of chicken comfort it sitting on the other hens' eggs. Fortunately, she is as sweet and good-natured in her broody mood as she is normally.
This morning another one of the hens kicked her off the nest, so I may be getting broody #2. I figure as long as they are keeping their health, they can brood all they want.