Found on steamykitchen.com, here are notes from the recipe:
I recommend using salted butter, which is all the salt that's needed to flavor the dish. If you're using unsalted butter, you might want to season with a bit of salt while cooking the tomatoes. An important tip is to make sure the butter mixture does not come to a boil - keep the heat low so that the butter emulsifies (turns into a nice, smooth creamy sauce) instead of breaking up.
Ingredients
1 3/4 pound live lobster or 2 uncooked lobster tails
2 tablespoons water
1/2 cup salted butter (1 stick), cut into 1 tablespoon chunks
1 clove garlic, very finely minced
2 tomatoes, cut into large chunks
few fresh basil leaves, chiffonade
Instructions
1. If you are using lobster tails: Use sharp kitchen shears to cut shell of lobster all the way down its back. Turn over and cut bottom shell all the way down. Peel off shell and remove meat. Continue with step 2. If using live whole lobster - bring a large pot of water to boil. Turn off heat and add the lobster. Cover with lid and let cook for 3 minutes. Remove all lobster meat from shell and cut into large chunks.
2. In a sauce pan, bring 2 tablespoons of water to simmer over medium-low heat. Whisk in 1 piece of butter. When butter had melted, add another piece. Continue with remaining butter pieces, one at a time. Make sure the mixture does NOT come to a boil, otherwise the butter will separate.
3. Keeping the heat on medium-low, add the lobster pieces and cook for 5 minutes, turning the lobster pieces every minute or so. Make sure mixture does not boil. Remove lobster pieces and divide amongst the 2 serving bowls.
4. In the same saucepan with the remaining butter, turn the heat up just a bit, add the garlic. When fragrant, add the tomatoes and cook for just a couple of minutes until the tomatoes have released some of the juices. I like to gently smash the tomatoes a bit so more juice comes out. Throw in the basil and you're done. Spoon tomatoes over lobster and serve immediately.