We've always done ours one of two ways: (These are Florida Lobsters) 1) Use a heavy knife to split the top shell length wise. Leaving the tail together (to hold the 2 halves together) From the front, pull the meat up thru the split, again leaving attached at the tail end. Squeeze the shell halves back together so the meat sits on top of the shell. This is easier than it sounds, and looks great!
Sprinkle some paprika on top (or any spice you like, cajun is great!). Grill meat side up in a closed grill. Paint with melted butter a couple times while cooking. When the meat becomes opaque, flip it to meat side down just long enough to give it a little brown.
Don't over cook, or they dry out.
2) You can also split them from the underside & cook shell side down with the meat still in the shell. Use the method as above. Its a little tougher to get the meat out when eating, but quicker to prepare and easier to manage on the grill.
Some of our friend like them wrapped in foil with the butter and spices in side. (you still need to split 'em), but where's the flavor?
It's a mortal sin the boil them.
(Time to go to the Keys!)