Keep monkfish cool on the trip from the market to your house. Never let it stay unrefrigerated for long. To store monkfish, remove packaging, rinse under cold water, and pat dry with paper towels. Fish deteriorates when it sits in its own juices, so place it on a cake rack in a shallow pan filled with crushed ice. Cover with cling wrap or foil and set in the coldest part of the refrigerator. Monkfish will store well this way for up to two days. When well-wrapped, monkfish can be frozen for up to two months in a refrigerator freezer and for three to four months in a deep-freeze. Use lined freezer paper and wrap fish tightly from head to tail with at least two layers of paper. To thaw slowly, unwrap, place fish in pan, cover, and leave for 24 hours in the refrigerator. To thaw more quickly, place the whole fish (wrapped in a watertight bag) in a sink with cool running water, allowing about 30 minutes per pound (about 454g). For fastest thawing, use the defrost cycle of your microwave, allowing 2 to 5 minutes per pound, with equal standing time in between zaps (as one minute defrost to one minute resting).