Put live crayfish in a bowl, cover with wet paper towels, and keep in the refrigerator for no more than 24 hours. Fresh crayfish is best cooked and eaten the same day you buy it, but will keep safely in the refrigerator for up to two days after it is cooked. To freeze, wrap crayfish meat carefully in freezer paper or plastic, and over-wrap with a plastic bag. Store for up to two months. To thaw, unwrap, place in a bowl or saucepan and cover and let thaw in refrigerator overnight. To thaw more quickly, wrap crayfish in waterproof plastic and place in a sink with cool running water, allowing about 30 minutes per pound (454g). For fastest thawing, place in a shallow microwave-safe bowl, cover and use the defrost cycle of your microwave allowing three to five minutes per 1/2 pound (227g).