For a more upscale aproach, I poach the lobster claws and tails in a saffron infused gee, and serve it with a grannysmith apple, vidalia slaw, finidhed witha vanillia and champagne vin.
One of my personal favorites is the classic old New England style roast. Lots of Lobster, corn on the cob, potatoes...mmmmmmm. Just done on hot coals and moist bulap to insulate. And served with boiled potatoes, and corn on the cob.
For quick and easy, just throw them on the grill and cook for 13-18 min over medium heat. You could boil them in a broth with alot of aromatics and stuff.
Thermador is a classic.
Cut in half, lengthwise, brush with clarified butter witha little lemon juice, lime juice, garlic and cilantro, and then grill them 4-6 min per side on med high heat.