Preheat oven to 375ºF. Butter bottom of a 9-by-13-inch baking dish. Arrange fish in dish, sprinkle with salt and pepper and dot with 1/2 Tbsp. butter. Bake until fish becomes opaque and tender when pierced with tip of a paring knife, about 10 minutes.
While fish is baking, melt remaining 3 Tbsp. butter in a small saucepan over medium heat. Add garlic and cook, stirring, until fragrant, about 1 minute. Stir in lemon juice, capers and tarragon, then drizzle sauce over fish and serve.