Pat the duck breasts dry. With a sharp knife, score the skin in a crosshatch pattern, being careful not to cut into the meat. Season with salt and pepper on both sides.
Place the breasts skin-side down on a cold pan. Turn the heat to medium and sear for about 8-10 minutes. Pour off the rendered fat.
Flip the breasts and cook on the other side for about 2-3 minutes. If you want a more well-done finish, you can place them in an oven preheated to 180°C (350°F) for another 5 minutes. Remove and let the breasts rest for 5-10 minutes to keep them juicy.