One time a while ago I was given two decks of umbra cards that were oval shaped and came in these hard plastic cases that looked like oblong eggs. They're the perfect diameter to fit two sponge balls in without crushing them, so I rarely have to water them and they're always ready to go.
In your pocket. If you don't have a really cheap set, you could keep them they're for a whole night without them getting flat and crushed up. Or you could use the back pocket if you won't be sitting down