I have 6 cages on an auto mister system. They each have a small drain in the middle that flows into containers. (2 of the cages are small 15x16x20 and I have a valve that reduces the water to their cages).
The misting is scheduled for 4 times a day at 2 minutes each. This seems to present enough opportunities for drinking so I do not use drippers.
I had 2 drippers set up but they left a lot of water so I stopped. I read in one post that you need to set up a container in the cage (with a screen top) to catch the drip water.
The only challenge I have is with my plants. All the misting really leaves them soaked which is not good! I was thinking of putting some sort of plastic over the base of the plant(s) and see if that keeps the water out.
Look forward to hearing other ideas on this . . .
Jim