Heat the butter in a large, nonstick frying pan until melted and starting to turn brown. Season the skate wings and add to the pan along with the capers. Cook for 3 minutes on each side until lightly browned and just cooked through. Transfer the skate to serving plates and spoon over the capers.
Stir the lemon juice and capers through the butter in the pan, then drizzle over the skate.