Rabbits are often caught in live catch metal cage traps. The sizes vary. I am assuming dimensions of about 7 to 8 inches tall, 7 to 8 inches wide and 16 inches long would be about right. You could see all around inside the cage trap that is made of wire. There is a door at one end that you open up and there is a long wire on it that is connected to a trigger or pan that is located at the back of the cage/trap. Bait, like apples, are placed in the back. The rabbit will enter the cage to get to the bait and step on the pan which will trigger the gate to close behind him. The most common live catch cage trap out there is Havahart. There are many good live catch cage traps out there though.
I see no one yet answered your question, so I thought I would try my hand at some typing.
I use to catch rabbits using snares. I have snared loads of rabbits in the winter when they established their trails. I use common picture wire as the snare. It works great. It also dispatches the rabbit at the scene as well. It is also capable of catching house cats too, so be careful where you use snares.
Good Fortune.
Snareguy-