A simple way to charcoal grill lobster tail starts with cutting the tail in the butterfly method with a knife or kitchen shears. Cut just down to the base of the tail without going all the way through. Heat a charcoal grill to medium heat, and season the lobster with olive oil, salt and pepper. Grill flesh down for five minutes, and then flip it. Cook until the flesh is firm or it has reached 135 degrees Fahrenheit.
Another method comes from Food Network. Combine 1 stick of salted, room temperature butter with 2 tablespoons of chopped chives, 1 tablespoon of chopped tarragon, 1 clove of minced garlic, a sprinkling of black pepper and a dash of hot sauce in a small bowl. Cover with plastic wrap, and set aside. Prepare a charcoal grill for direct medium heat grilling.
Butterfly 4 lobster tails, and insert a metal skewer to force the tail straight. Brush the tails with olive oil, and salt and pepper to taste. Grill flesh-side down for about five minutes or until shells brighten in color. Flip the shells over, and add a generous amount of the herb butter. Grill for another four minutes or until meat is firm and opaque.
Serve with more herb butter, lemon wedges and sprigs of chives.