In a medium saucepan, melt 1 tablespoon of the butter over low heat. Add the shallots and saute slowly, until soft. Add the dried cherries, molasses, pepper, and duck stock. Simmer 15 minutes.
Blend the arrowroot with the 1/4 cup of the Madeira. Mix the Madeira into the duck sauce and simmer 3 to 4 minutes, until slightly thickened. Set aside. (The sauce may be made ahead, up to this point.)
Preheat the oven to 425 degrees.
Season the duck cavity with the salt and pepper. Pierce the skin thoroughly around the lower breast, back, and thighs. Truss the duck and place, breast side up, on rack in shallow roasting pan. Place the duck in the oven and bake for 15 minutes. Reduce the heat to 350 degrees and roast the duck 30 minutes per side. With a bulb baster, remove some of fat that accumulates as the duck roast. Turn the duck, breast side up, and sprinkle with salt. Roast 10 to 15 minutes longer for medium rare or until juices run rosy when a thigh is pierced with a fork. For well done, roast until juices run clear.
Remove the trussing. Place the duck on a serving platter and keep warm in a turned off oven while finishing the sauce. (The duck may be roasted in the morning, if desired, and reheated at 300 degrees at this point.) Place under a broiler for 3 to 5 minutes for extra crisp skin.
Remove all but 1 tablespoon fat from the roasting pan. Add the remaining 1/4 cup Madeira to the drippings in the pan. Boil rapidly, scraping the brown bits from the bottom and reducing the wine to 2 tablespoons. Strain the wine reduction into the prepared duck sauce. Finish the sauce with the sherry vinegar. Simmer 1 to 2 minutes and swirl in the remaining 1 tablespoon of butter.