Preheat your grill to medium-high heat.
In a small bowl mix the butter, chives, tarragon, minced garlic, salt and pepper. Blend thoroughly. Cover with plastic wrap and set aside.
Using kitchen shears, cut the top of lobster tails straight down the middle of the shell. Cut the meat down the center without cutting all the way through. Using your hands spread the shell apart and gently loosen the tail from the bottom part of the shell. Insert a wooden skewer down the lobster tail so the tail stays straight. Brush the lobster meat with olive oil and season with salt.
Grill lobsters cut side down over medium high heat about 5 minutes, until the shells are bright in color. Turn the tails over and spoon a generous tablespoon of herbed butter onto the butterflied meat. Grill for another 3 minutes, or until the lobster meat reaches an internal temperature of 135 degrees using a thermometer.
Remove lobster tails from the grill and serve with more herb butter and lemon wedges.