Make sure that any clams (or other bivalves) you purchase smell very fresh and are not opened or cracked. Discard any that are either open or cracked.
Arrange the clams on the grill grate, nestling them in so that they sit flat and the juices remain in the shells. Close the lid and cook for 3 to 4 minutes (see above for cooking times for different-sized clams), until the clams open and are just barely cooked through. The best way to remove the clams from the grill is with tongs, and you should try and keep your hand steady so that as much of the juices in the bottom shell stay there for slurping.
Transfer them to a platter and serve hot with the lemon wedges.
Notes
You can grill basically any type of clam. There are three kinds of clams on the grill here: Littleneck, Cherrystone, and Topneck. Quahogs, chowders, manillas, and coquinas are also all great candidates for grilling. The more locally you can get your clams, the fresher they will be!
You’ll have to detach the clam from the top shell to eat it. Then pour the liquid from the bottom shell into your mouth as kind of a chaser. Just try not to spill the juices! Serve the clams on a large platter with some crusty bread for soaking up the juices.