In a small bowl blend butter, chives, tarragon, minced garlic, hot sauce, and black pepper with a rubber spatula. Blend thoroughly. Cover with plastic wrap and reserve.
Using kitchen shears, butterfly the lobster tails straight down the middle of the softer underside of the shell. Cut the meat down the center without cutting all the way through. Insert a metal skewer down the lobster tail so the tail stands straight. Brush the tails with olive oil and season with salt, to taste.
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 4 minutes, or until the lobster meat is an opaque white color.
Remove lobster tails from the grill and serve with more herb butter and lemon wedges. Garnish with chive sprigs.