For the best flavor, serve cheese at room temperature. Remove cheese from the refrigerator 30 - 60 minutes prior to serving. Large cheeses require a longer time to reach room temperature than soft-ripened cheeses. Only remove the amount of cheese you will be using from the refrigerator.
If you are serving individual portions, it is easier to cut the soft cheeses while they are still cold. Bring them to room temperature after they are cut.
If you are presenting cheeses on one cheese platter, don't cut them into individual servings advance. it is best to let guests slice their own portions. Be sure that cheeses on a plater have sufficient room between one another to allow for easy cutting or slicing. Try to have individual knives or serving tools for each cheese served. Avoid placing strong, pungent cheese right beside delicately flavored cheeses.
Keep the cheese wrapped so it doesn't dry out when storing. Unwrap it just before serving. Wrap and refrigerate any leftover cheese as soon as possible.
Plastic wrap is acceptable for wrapping cheese. Some purists believe that plastic wrap does not allow the cheese to breathe. They will only use wrappings such as waxed paper, parchment paper, butcher paper or aluminum foil. If cheese is wrapped in plastic, the wrapping should be changed every few days to allow the cheese to breathe, and to keep the cheese from becoming slimy or discolored.
Different types of cheese require different methods of storage:
Hard cheeses with little moisture (such as Parmesan, Dry Jack) should be wrapped to avoid further moisture loss using plastic wrap.
Semi-hard cheeses (such as Cheddar, Jack, Swiss) can be wrapped in either plastic or waxed paper or parchment paper.
Semi-soft cheese (such as Brie, Gorgonzola) should be wrapped in parchment or waxed paper, or may be kept in a plastic container.
Soft or fresh cheeses (such as Ricotta, Feta) should be kept in a plastic container.
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(Source: American Cheese Society, Beecher's Handmade Cheese, Wisconsin Cheese Makers Association)