One easy recipe for lobster tails is broiling, where you expose the meat in the shell, coat it with olive oil or butter, and place it under an oven broiler for approximately 10 minutes. Also try baking butter-coated lobsters in an oven at 350 degrees Fahrenheit for 15 minutes.
Many lobster tails come frozen, so you want to thaw the product overnight to prepare it for cooking. Some methods call for the lobster to be only partially thawed in order to get the tenderest result; some experimentation with your particular oven may be necessary. For safety, open lobster tail shells with scissors rather than a knife and go lengthwise down the back. Whether baking or broiling, make sure lobster tails are facing meat-side up while in the oven.
In addition to butter, consider flavoring the tails with lemon juice, salt and pepper to taste, along with fresh herbs, such as sage, basil or tarragon. Freshly minced garlic or Cajun seasoning are also possible accompaniments. For a simple brown butter sauce, melt 8 tablespoons unsalted butter over medium heat until the milk solids brown slightly, then add some shallot, parsley and lemon zest to baste or dip tails after cooking. Remember that undercooked lobster is dangerous, so there shouldn't be any translucency remaining in the finished tails.