With a sharp paring knife, score the skin in a criss-cross pattern, making cuts about 1/2 inch apart. Cut down into the fat without exposing the meat, leaving about 1/8 inch of fat uncut. (This is tricky because the fat is tough, but you make some of the cuts down as far as the meat like I did, the fat will still tend to stay intact on the breast.) Salt both sides of the breasts.
Place a heavy skillet over medium high heat. Add the duck breasts, skin side down. Cook without moving them for about 6 minutes or until the skin is well-browned.
Transfer, skin side up, to a roasting pan or rimmed baking sheet with a roasting rack. Reserve the fat in the pan for another use, such as roasted vegetables.
Place roasting pan with the duck breasts in the preheated oven. For very rare, roast until the internal temperature in the thickest part reaches 135ºF (start checking at about 25 minutes). For medium rare to medium, roast until temperature reaches 145ºF to 150ºF (check at about 50 minutes).
Place breasts on a cutting board and let rest for about 5 minutes before slicing. Cut into 1/4-inch to 1/3-inch slices. Serve with a drizzle of balsamic-grape sauce, if desired.