I have one cup, it's a double walled titanium mug so no burnt lips when drinking hot liquids. I made an aluminum foil top for it. To keep the top from getting crunched, I simply put the top of the mug into a small stuff sack, followed by the mug. Does a great job of keeping the top mangled-free. (My whole cook kit goes into stuff sack, it's not just for the mug).

I'm not sure about the size of your mug, but you could also look at the Caldera Caddy on Trail Designs' website, the smaller one might work for what you're looking for.