Preheat grill to medium-high heat (350° to 400°). Make 3 parallel cuts, slicing into the flesh at an angle, about 1 1/2 inches apart on each side of each fish, slicing down to the bone. Season skin and cavity of each fish with salt and pepper; coat each fish with 1 tablespoon oil. Stuff cavity of each fish with 1 tarragon sprig and 2 or 3 tangerine slices. Tuck 1 tarragon sprig and 1/2 of a tangerine slice into each of the slits.
Brush grill grates with oil. Place fish directly on grates; grill, without moving, 4 to 5 minutes or until skin no longer sticks to grates. Carefully turn fish using an oiled metal spatula; grill 4 minutes or until done. Transfer to a platter, and serve with tangerine wedges.