Live littleneck clams are encased in tightly shut shells. Discard any clams with loose or partially open shells. Prior to grilling, store clams in a bowl covered with a moist dish cloth or paper towel in the refrigerator, where they will remain alive for several days.
Scrub clams under cold running water. In a 6- to 8-quart Dutch oven, combine 4 quarts cold water and 1/3 cup of the salt. Add clams; soak for 15 minutes. Drain, discarding water. Rinse clams. Repeat soaking, draining, and rinsing two more times.
Meanwhile, in a small bowl stir together butter, lemon peel, tarragon, and pepper. Beat with an electric mixer on medium speed until well mixed. Stir in capers.
For a charcoal grill, grill clams in a single layer on the rack of an uncovered grill directly over medium-hot coals for 5 to 8 minutes or until clams open at least 1/2 inch, turning once halfway through grilling. Remove clams as they open and keep warm while others cook. (For a gas grill, preheat grill. Reduce heat to medium-high. Place clams on grill rack over heat. Cover and grill as above.) Discard any unopened clams. Serve clams with butter mixture.