Squeeze the lemon or lime over both sides of the fish fillets and season the fish with salt.
Combine the panko and Parmesan in a small bowl and sprinkle over both sides of the fish, generously coating the fish all over. Press the Parmesan mixture into the fish so it sticks.
Heat butter and olive oil over medium heat in a non-stick frying pan. Once melted and foaming, add fish in a single layer (you may have to do this in batches depending on the size of your pan). Cook for 2-3 minutes per side or until the crust is golden brown and fish is firm to the touch.