In a medium skillet, saute the celery, onions and sweet red pepper in butter until tender. Add the salt, pepper, tarragon, basil and milk; mix well. Cook for 1 minute, stirring constantly until thickened. Add the cheese and stir until melted. Do not boil.
Rinse the Tilapia fillets in cold water and drain thoroughly. Place the fish in a 12 x 8 x 2 inch bakingdish;spoon the sauce evenly over the fish. Bake at 425 degrees for 8 to 10 minutes, or until the fish flakes evenly when tested with a fork.