Preheat the oven to 400 degrees.
In a small saucepan heat the port over moderate heat until it is hot. Add the cherries, cover the pot and let the mixture stand for 15 minutes.
Score the skin of the duck in a crosshatch pattern and season both sides of the duck with salt and pepper. Heat a medium saute pan over high heat until it is very hot. Add the duck, skin side down and reduce the heat to moderately low. Cook the duck, pouring off the accumulated fat from time to time to a small roasting pan and roast it for 10 minutes for medium rare. Let it stand for 10 minutes before slicing.
While the duck is roasting, pour off all but 2 tablespoons of fat from the saute pan. Add the shallots and saute over moderately high heat until softened. Add the rhubarb and saute for 5 minutes. Transfer the mixture to a bowl. Add the cherry/port mixture to the saute pan and let it simmer for 1 minute. Add the chicken stock and simmer until reduced by one third. Whisk in the arrowroot mixture and let the sauce come to a boil. Add the pepper and salt to taste. Let sauce simmer until thickened. Return reserved rhubarb mixture to pan and heat through.
Slice the duck at an angle and divide among 4 plates. Serves each portion napped with some of the sauce.
Serve with sugar snap peas and garlic mashed potatoes.
Recipe courtesy of Gourmet Magazine