Season flour with salt and pepper. Dredge both sides of fillets in flour. Shake off surplus flour.
Heat saute pan over medium heat. Add olive oil and 1/4 cup clarified butter. Add fillets, flesh side down, to pan. Cook 6 minutes. Turn, and cook the other side for 4 minutes. Remove fish from pan to platter. Strain cooking juices and set aside. Return fillets to pan, flesh side up.
Meanwhile, in another pan, add remaining clarified butter. On medium-low heat, add tomatoes. Then add garlic. Stir gently. Stir in 1/4 teaspoon tarragon, 1 teaspoon dill, and the parsley. Add 1-ounce of Pernod, wine vinegar, and salt and pepper. Simmer gently. Add fish juices. Increase heat to high.
Season fish fillets with remaining dill and 1/4 teaspoon tarragon. Add remaining Pernod to pan with fish and set aflame.
Stir in butter to sauce and pour over fish. Remove from heat, slide onto platter, and serve immediately.