Cut each cantaloupe half lengthwise into 3 wedges (6 total). Shave thin slices from seeded side of a melon wedge with vegetable peeler (first slice may be irregular), stopping when you get close to rind. Arrange slices, overlapping slightly, on 1 plate. Repeat with remaining cantaloupe, putting slices from each wedge on a separate plate.
Drizzle each serving with 1/4 teaspoon lime juice and 1/2 teaspoon oil, then scatter 10 tarragon leaves on top. Season with sea salt and pepper and serve with lime wedges.