Spread carrots and shallots evenly in a 12-inch heavy skillet, then dot with butter and sprinkle with salt.
Whisk together water, broth, Port, and honey and pour over vegetables. Cover skillet with a lid (or tightly with foil) and simmer over moderate heat until vegetables are tender when pierced with a paring knife, about 20 minutes.
Transfer vegetables with a slotted spoon to a bowl and boil liquid over moderately high heat, uncovered, until syrupy and reduced to about 3 tablespoons, about 15 minutes. Return vegetables to skillet and gently stir to coat with glaze.
Sprinkle with dill and chives (if using) and pepper.