For preventing the opened ham and cheese from drying out. I tried a container called "Ham Fresh Keeper FKH1" sold by skaters.
A container of a size (approx. 138 x 120 x 32 mm) that matches commercially available sliced ham and cheese. It comes with a drainboard with multiple holes, making it easy to take out the last piece of ham or cheese. The container has a handle so it's easy to hold and take it out of the refrigerator. It is not compatible with microwave ovens, so be careful not to accidentally use it for warming up!
It is sold on various mail order sites and the price range is around 300 yen. If you find that opened ham and cheese often dry out in the fridge, why not give it a try?