Cheese is easiest to grate if you allow it to thaw somewhat first. Place a frozen block of cheese in your refrigerator at 40 degrees Fahrenheit or cooler. The cheese will be soft enough to grate within a few hours. Freezing cheese causes it to dry out slightly and become crumbly or mealy, so even with thawing, the cheese may not grate well. You might not even need to grate the cheese. If you merely cut it, it will crumble into small pieces. Set it on a cutting board and cut the pieces as if you were dicing vegetables. The pieces won't be quite as small as shredded cheese, but they work fine for melting in a casserole or soup.

Frozen cheese, in any form, is not particularly pretty when thawed, but it tastes fine. You can't cut it into nice cubes for a salad, for example. Nor can you create fine, even shreds for tacos, because it crumbles. Use previously frozen cheese for cooked dishes instead. As it melts, any imperfections in appearance will disappear.

The best types of cheese for freezing are hard cheeses, such as gouda, Parmesan and cheddar. These cheeses have low moisture and tend to retain their flavor and texture best. These cheeses are also the best candidates for grating. Avoid freezing soft, delicate cheeses, which may become watery or mushy in the freezer or develop off-flavors. Freeze small blocks of cheese, weighing no more than 1/2 pound. Wrap cheeses tightly in foil or plastic wrap or seal them in heavy freezer bags. Freeze cheese for no more than six months.

A better strategy for freezing cheese is to grate it before you freeze it. Grate the cheese and toss it with a bit of cornstarch in a bowl. The cornstarch prevents it from clumping together in the freezer. Pack the grated cheese in heavy freezer bags or vacuum-seal bags. Squeeze out as much air as you can, and label the packages with the date. Use them within three to six months. Thaw shredded cheese in the refrigerator for a few hours before use.