To prepare: In a pot large enough to hold the duck, combine port, 2 cups water, 1/4 cup of sugar, and honey; bring to boil.
Meanwhile, season duck cavity with salt and black pepper; truss duck; set aside.
When wine mixture comes to a boil, remove from heat. Add duck; let marinate at room temperature for 20 minutes, turning occasionally.
Preheat oven to 350° F.
Remove duck from marinade; place on a rack in a shallow roasting pan. Bake until duck is brown and reaches internal temperature of 185° F, about 1 hour 15 minutes. Let stand at room temperature for 10 minutes.
Meanwhile, in a medium skillet, heat olive oil until hot. Add shallots; cook, stirring frequently, until soft, for 3 to 5 minutes. Add remaining 1/2 cup sugar; cook over low heat, stirring frequently, until sugar is dark brown, 10 to 15 minutes.
Stir in vinegar, brandy, blueberries and tarragon. Cook over medium-high heat until blueberries are soft, about 5 minutes. Add stock; bring to a boil; boil until reduced by half, about 20 minutes. Season to taste with salt and pepper.
To serve: Carve duck. Spoon blueberry sauce over duck. Garnish with fresh blueberries, if desired.
Serves 2 to 3 with 1 1/2 cups sauce