Once a cheese has been cut into, it can be a bit tricky to properly store what's left, especially if you have cut a waxed or bloomy-rind cheese. Here are some tips:
Hard Waxed Cheeses
Wrap the remaining portion of the cheese loosely in waxed paper, then in plastic wrap. You can then place it into a covered container and keep it either in the ripening area or in the refrigerator.
Cheeses Packed in Brine
Cheeses that must be stored in brine should stay in brine when not being eaten. Cut your portion out and replace the cheese into the brine. You can use a zipper-style bag to keep the cheese packed in brine. If the brine gets cloudy, you can make new medium brine to store it in.
Keep vacuum sealed cheeses in an airtight container with a lid or a zipper-style bag.
Surface-ripened or Bloomy-rind Cheeses
Keep surface-ripened cheeses loosely wrapped in cheese paper. Or, you can use a container with holes drilled in it. Just remember that these cheeses need to breathe, and store appropriately.
These cheeses are best when they are wrapped in cheese paper and/or stored in boxes. If you cannot find a suitable box, you can just cover the cheese paper wrapping with plastic wrap.
Keep these mold-ripened cheeses away from oxygen to avoid overgrowth of the blue mold. If you keep the cheese stored at a temperature lower than 40°F, you will successfully retard the growth of the mold. These cheeses can be wrapped in plastic wrap then tightly wrapped in foil.