Keep in mind, cardboard does not actually have 100% the nutrition they need. Then again, it probably varies. I know toilet paper rolls are really bad for that. They'll eat it, but it doesn't have as much nutrition for termites as a piece of rotten wood does and is likely to just kill the colony. I'd personally offer them alternatives as well.
But, other than that...termites are really easy to keep. I kept a desert variety found in California and I literally forgot them for an entire year because they got buried in moving boxes. So, they had no water for one whole year and were in a VERY hot and dry garage. I look in and see tons of nymphs all over. I thought they'd all be dead with not a hint of water. I wouldn't do that with yours, though. 
Your termites are probably going to be Eastern subterranean termites, which are most common over where you are. I think it might be the only subterranean termite species where you are located, but I'm not sure. I know California has a whole bunch of species of termites. But, just put them in a glass tank or whatever with a bunch of soil and wood, and make sure its kept moist. Most termites dry out really quick and die without moisture. Be patient and then wait for some amount of months for nymphs to show up. It usually takes a lot longer to get nymphs than it does waiting for ants to eclose.
Oh, and make sure there isn't any ink or dye or anything like that on any pieces of wood you put in there. And no treated wood. If, say its cardboard that has ink on it (like toilet paper rolls tend to have some ink writing on it) that can and likely will kill the termites. You can know if the wood is treated if it has a green (sometimes blue) tinge on the ends of it.
Edited by Vendayn, March 30 2015 - 11:23 AM.