What's the point? You won't get any grill flavor into a closed shell, and when they are open, they are done.
If you want to cook them on the grill, put them in a pan with a little water and steam them.
As for a sauce? Garlic butter with a little lemon is pretty darn good!
Linda C

These are on my list of "recipes to try" so I can't say it's a tried & true recipe but it sounds good. I wonder if throwing some soaked hickory chips on the hot lava rocks would add something extra to the flavor??--Ann

Grilled Steamed Mussels and Clams

2 lbs mussels well rinsed under cold running water
2-1/2 lbs littleneck clams (about 24) well rinsed under cold running water
8 T (1 stick) unsalted butter
¼ cup chopped parsley leaves
4 cloves garlic, peeled and minced
1 tsp hot red pepper flakes
½ cup white wine
¼ cup freshly squeezed lemon juice

Discard any mussels or clams with broken shells as wellas those whose shells remain open after you tap them lightly. Prepare a charcoal fire or gas grill for direct grilling over high heat

Cut 4 sheets of heavy duty alum foil each 18 x 24". Set them flat on a work surface. In the center of each sheet of foil, pile ¼ of mussels (about 12) and ¼ clams (about 6). Cut butter into small pieces and dot each mound of shellfish with about 2 T of butter. Sprinkle each mound with ¼ of parsley, garlic and red pepper flakes. Pour 2 T of wine and 1 T lemon juice over each pile of shellfish.

Bring up the 2 long sides of the packets and fold them over each other 2 or 3 times at the edge where they meet to seal, leaving some room inside for the mussels and clams to expand as they cook. Fold the shorter ends of the foil over themselves 2 or 3 times as well. The packet should be well sealed. Carefully transfer the packets, seam side up, onto the grill and cook until the shellfish open, 8-10 minutes. (youÂll have to peek into one packet to make sure)

Serve mussels and clams in the foil packets with crusty bread for mopping up the sauce or if you want to be more elegant, put the shellfish in a bowl, pouring the packet juices on top. You can also serve the mussels, clams and their juices directly over cooked linquine. Make sure to discard any of the shell fish that do not open after cooking. Makes 4 servings.

source: Al RokerÂs Big Bad Book of Barbecue

Ann, although that does, indeed, sound tasty, nothing is served particularly by cooking on a grill. Other than you get to cook outside.

If you want to experiment, wrap the four packets as directed. Then cook one on a gas grill, one on a charcoal grill, one on your indoor rangetop, and one in the oven.

I suggest that all four will taste exactly the same.

There is a fairly large coterie of people who have convinced themselves that anything cooked on an outdoor grill tastes better. Lot's of luck on that one. It just isn't true. And it's particularly not true if you use a gas grill instead of charcoal.

Most of the time, whole shellfish is one of those things that is not effected by the cooking method.

Here's a good sauce for mussels from Craig Claiborne

SAUCE RAVIGOTE (about 1 1/2 cups)
3 TBL chopped shallots
1/3 cup chopped capers
1 TBL chopped fresh tarragon
2 TBL chopped parsley
1 cup broth in which mussels cooked (Or some clam juice would work)
1/2 cup mayonnaise
3 TBL Dijon or Dusseldorf mustard
1/4 tsp Tabasco
Pepper to taste

Combine the shallots & capers in a mixing bowl. Add the tarragon & parsley. Reduce the broth by 1/2 by boiling over high heat. Add the mayo to the bowl & using a whisk, beat in the hot liquid. Add the mustard, Tabasco & pepper. Cool sauce to room temperature & pour over shelled mussels & serve.~~