Combine the carrots, water, 1½ tablespoons tarragon, butter, vinegar and honey in heavy large skillet. Bring to boil. Reduce heat to medium-low; cover and simmer until carrots are almost tender, about 12 minutes.
Uncover and continue cooking until the carrots are tender and the liquid is reduced to a glaze, about 6 minutes longer. Season with salt and pepper.
Transfer the carrots to a platter and sprinkle with the remaining 1½ tablespoons tarragon. Serve immediately.