Combine the butter, cilantro, lemon or lime juice, zest, salt and pepper in a bowl and beat by hand with a wooden spoon. Shape into a rough log about 2 inches long and 1 inch in diameter, wrap in plastic wrap and chill until firm.
Prepare a fire in the grill. Position the oiled rack 4–6 inches above the fire.
Rub the fish lightly with oil and sprinkle to taste with salt and pepper. Arrange the fish on the grill. Cook, turning once, about 10 minutes; the fish is done when it turns from translucent to opaque throughout. Remove to a warmed platter or plates. Cut the cilantro butter into 4 equal slices and top each fillet with a slice.