For the cocktail sauce: Combine the chili sauce, horseradish, Worcestershire sauce, lemon juice, salt and pepper in a bowl. Chill until serving.
For the crab: Drop both whole live crabs in a large pot of salted boiling water. Let cook until the shells turn a bright red, 10 to 15 minutes. Be aware that the meat cooks very fast once exposed to the hot water. Remove the crabs from the water and pull the main shell off. If this is difficult, insert a large knife between the shells in the back of the crab where they meet and pry open. Once the top shell is removed, rinse the crab in the sink, cut in half (from front to back, not side to side) and peel off the gills (which are attached to the bottom portion) and discard. Clean out all entrails and other waste from the top shell portion. Place on a plate with the lemon and lime slices, and place the top shell back on top for presentation. Serve with the cocktail sauce.
This recipe was provided by professional chefs and has been scaled down from a bulk recipe provided by a restaurant. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.