Thaw fish, if frozen. Rinse fish; pat dry. Sprinkle lightly with salt and pepper; set aside. In a large skillet cook fennel, onion, carrot, and garlic in hot oil over medium heat for 7 to 9 minutes or until vegetables are tender and light brown. Remove from heat. Stir in dillweed, the 1/4 teaspoon salt, and 1/4 teaspoon pepper. Stir in wine.
Reserve 1/4 cup of the vegetable mixture; spoon remaining vegetable mixture into a 2-quart square baking dish. Place fish on top of vegetables, tucking under any thin edges. Spoon reserved vegetable mixture on top of fish.