Wrap each duck breast in plastic wrap and pound them with a meat mallet until each breast is about 1 inch thick. Place the duck on a plate, sprinkle both sides with a total of 4 teaspoons salt, cover with plastic wrap, and refrigerate for at least 6 hours or overnight.
When ready to cook the duck, preheat the oven to 375 degrees F.
Score the skin of the duck breasts with a sharp knife, making a crosshatch pattern but not cutting down to the meat.
In a large (12-inch) heavy-bottomed, ovenproof skillet, heat the oil over medium heat. Place the duck breasts in the pan, skin side down. Cook uncovered over medium heat for 12 to 15 minutes, discarding the fat from the pan occasionally, until the skin is very browned. Turn the duck with tongs, place the skillet in the oven, and roast for 12 to 18 minutes, until the internal temperature of the duck is 120 degrees F for rare. Remove from the oven, cover the pan tightly with aluminum foil, and allow the duck to rest for 10 minutes.
Meanwhile, make the sauce. Melt the butter over medium-high heat in a medium saucepan. Add the shallots and saute for 2 minutes, until tender. Add the vinegar and cook for one minute. Add the Port, chicken stock, cherries, 1 teaspoon salt, and 1/2 teaspoon pepper, bring to a boil, lower the heat, and simmer for 15 minutes. Stir in the crème fraîche, orange zest, and orange juice and keep warm over low heat.
Transfer the duck to a cutting board and slice diagonally, fanning the slices out on 4 dinner plates. Spoon the sauce generously on top, sprinkle with salt, and serve hot with extra sauce on the side.