I am assuming you purchased them in a grocery store where there is a seafood dept and an occasional tankful of live lobsters. The tails you purchased are red. They are already cooked. Yes thaw them for warming and eating. Usually reheating the already cooked lobster is enough. Trying to cook them again by broiling is going to make them tough as an old boot.

I am married to a man from MA and his family have owned lobster boats for generations. (On a side note Lobster different ways 4X a week is boring.) They have all told me "Never ever buy frozen cooked lobster in the grocery store." I asked "why?" so these fine folk gave me many reasons and now that I know why. I will not buy frozen cooked lobster in a grocery store ever. The things I learned are not fit for printing on public venue. I am not normally a squeamish type but what I learned made my hearty stomach turn. It was years before I could walk pass the lobster tank or think about getting a lobster again. Fresh out of the sea is expensive if you don't live on a coast but you"ll never know how tasty lobster is until you have eaten it from the dock.
LIL

Procedures to Cook Frozen Lobster Tails

Defrost the Lobster Tails
The first step in cooking frozen lobster tails is to thaw the lobster completely. Defrosting is essential prior to cooking because it helps in maintaining the flavor of the lobster tails. You may cook lobster with ice intact, but the resultant meat will be less delicious than the one which has been thawed before.

When you get the lobster tails from the market, keep them in the refrigerator for a day. Remember not to take out the lobster tails from the packaging before keeping in the refrigerator. After twenty four hours, the lobster tails will get defrosted. Another method to defrost the lobster tails is to keep them in water for some time. This is a quicker way to defrost them. While defrosting in water, keep the lobster tails in storage bags before immersing them in water so that the water does not reach the meat and render it tasteless. Some people even use an oven to defrost the lobster tails, but I personally will not recommend it as the lobster might lose its softness because of the heat in the oven.

The best way to cook frozen lobster tails is by thawing it in a refrigerator overnight, before cooking. After the lobster tails have been thawed, you may choose any of the lobsters recipes to cook frozen lobster tails of your choice.

Bake the Lobster Tails
To cook frozen lobster tails which are baked, you have to use an oven. Start with pre-heating the oven to 400 degrees Fahrenheit. Meanwhile, wash the lobster tails with cold water, after they have been thawed, using the methods mentioned above. After washing and drying them, put them on a baking sheet. Now make a lengthwise cut on the shell in such a way that the meat is visible. Now keep the lobster tails for baking in the oven for about ten minutes. Take the meat out after ten minutes, sprinkle salt, pepper and some herbs such as oregano on top of it for taste. A scrumptious, tender, baked lobster tail is ready. Read more on lobster roll recipes and lobster meat recipes.

Steam the Lobster Tails
For cooking frozen lobster tails which are steamed, first of all clean the lobster tails with cold water so that the germs and bacteria are washed away. Once the lobster tails have been cleaned and dried, skewer the lobster tails before setting them up for steaming in a steamer. This is done so that the lobster tails do not curl upon steaming. Now put the lobster tails in the steamer and cook for about three minutes. Remember to leave enough space in between the lobsters while steaming so that they are cooked on all sides. Read more on how to steam a lobster.

For steaming, you may put water or beer or white whine in the steamer. Alternately you can make a sauce by mixing wine, cream and paprika and steam the lobster in it. After the steaming has been done, put the lobster tails under cold water for a while. Steamed lobster tails are now ready to be served. Just like a steamed lobster, grilled lobster is also quite tasty. To know how to grill lobster tails, read grilling lobster tails.

Thanks, all. I bought them frozen and they they are not red, not pre-cooked. They are very dark brown-gray. So I'm thawing now. I realized they must be thawed first because I plan to cut the shell to expose t6he meat for cooking. That won't work if I leave them the way they are, frozen. Plus I do want to thoroughly rinse them clean. Thanks for all your responses.

Hi Jannie,
I just went through this in February when Bill brought home lobster tails for Valentines Day. I found this really great site....posted below and this was the recipe that I used. They were awesome!

Grilled lobster tails
Insert a wooden skewer into the lobster tails to prevent them from curling on boiling.
Prepare a large saucepan of salted water according to instructions above for boiling lobster tails.
Once the water has reached a fierce boil, drop the tails in and cook for 4 minutes.
Drain the tails and position them on their backs once they have cooled slightly.
With a sharp knife, split the soft top shell of the tail, lengthways down the middle, but leave the hard shell underneath in tact.
Pour some melted butter and lemon juice over the meat of the tails or brush a marinade of lemon juice, olive oil, salt pepper, garlic powder and paprika over the meat and place shell side down into a pre-heated grill.
Grill for approximately 7 - 8 minutes under a medium - hot heat or until the meat is opaque, no longer transparent and firm to the touch.
If you wish, you may turn the tails over half way through cooking.
Remove from the grill and serve hot with lemon, melted butter or mayonnaise

Good luck and enjoy!
Patti

Here is a link that might be useful: Cooking Lobster Tails