Lightly salt and pepper fillets. Dredge in flour.
Heat oil in a large skillet. Add butter and heat. Sauté fish, flesh sides down, until done, about 4 to 5 minutes. Turn over and repeat. Serve with lemon-butter sauce.
While fish is cooking, prepare lemon-butter sauce.
In a small saucepan, melt butter over medium heat. Stir in lemon juice, zest and pepper. Add fresh tarragon, mix well. Keep warm until ready to use, but do not continue to cook. Serve over fillets.
Contributed by Joyce Taylor