Heat oven to 350 degrees; heat a medium saucepan of water to a boil.
Starting at the large cavity end of each duck, separate skin from breast meat as much as possible by working your fingers between skin and meat, being careful not to tear. Prick skin all over with a fork. Place ducks breast side up in a large deep roasting pan. Rub each duck inside and out with coarse salt. Divide onions and celery between cavities. Sprinkle 1/2 cup of the sugar around the ducks. Pour enough boiling water over ducks (to help tighten the skin) to reach halfway up them; don't fill roasting pan to more than 1 inch from rim. Cover pan tightly with heavy-duty foil; braise in oven 1 hour. Remove pan from oven; remove foil. Carefully turn ducks over, using one large wooden spoon to turn each duck and another inside cavity to hold it. Cover with foil; braise until meat is tender but not falling off the bone, about 1 hour.
Transfer ducks to two large plates. Drain any juices inside ducks back into pan; transfer pan juice to a large bowl. Return ducks to roasting pan, breast sides up; let cool. Refrigerate duck and juices, uncovered, 4 hours. Remove fat from chilled pan juices.
Remove zest from 2 large or 4 small clementines with a vegetable peeler; cut zest into fine strips. Blanch the strips in a small saucepan of boiling water 5 minutes; drain. Squeeze enough juice from remaining clementines to measure 2 cups. Pour through a fine-mesh sieve into a 3-quart heavy saucepan. Add vinegar and remaining 2 tablespoons of the sugar; heat to a boil. Cook until reduced to about 1/3 cup, about 25 minutes.
Transfer 1 tablespoon of the glaze to a cup; reserve. Stir zest strips and 1 cup of the pan juices into glaze remaining in pan; reserve.
Heat oven to 500 degrees. Roast ducks, uncovered, until skin is crisp, 25-35 minutes. Brush reserved tablespoon of the glaze over ducks; transfer ducks to a platter. Pour off all but 1 tablespoon of the fat from roasting pan; set roasting pan over 2 burners. Add shallots; cook over medium-low heat, stirring, until softened and pale golden, 3-5 minutes. Add 2 cups of the reserved pan juices (reserve any remaining juices for another use); heat to a boil. Cook, scraping up brown bits, 2 minutes. Pour through a fine mesh sieve into the glaze and zest mixture; heat to a boil.
Stir together liqueur and arrowroot in a small cup until smooth; whisk into sauce. Simmer, whisking occasionally, until thickened, 3-5 minutes. Season with salt and pepper to taste. Serve duck with sauce; sprinkle with pistachios.