Remove giblets and neck from ducklings; reserve for other uses. Rinse ducklings thoroughly with cold water; pat dry. Prick fatty areas of ducklings with a fork at intervals. (Do not prick breast.) Lift wingtips up and over back, tucking under ducklings securely.
Combine butter and lemon juice, stirring well. Place 2 tablespoons of the butter mixture inside the cavity of each duckling. Rub outer skin of each with 2 tablespoons butter mixture. Set remaining butter mixture aside. Close cavity of ducklings with skewers; truss. Fold neck under and place ducklings, breast side up, on a rack in a large roasting pan. Bake, uncovered, at 425° for 45 minutes. Brush ducklings with remaining butter mixture. Continue baking for an additional 45 minutes or until drumsticks and thighs are easy to move. Set ducklings aside; keep warm.
Skim fat from pan drippings. Discard fat, and place 1 cup drippings in a medium saucepan; gradually add flour, stirring well. Cover, and cook over medium heat, stirring constantly, until thickened and bubbly. Set aside.
Grate 1 tablespoon orange rind; squeeze 2/3 cup juice from Seville oranges. Combine rind and juice; set aside. Reserve remaining orange for garnishing purposes, if desired.
Sprinkle sugar in a heavy saucepan; cook over medium heat, stirring constantly with a wooden spoon until sugar is melted and golden brown. Stir in vinegar and orange juice mixture. Add juice mixture to thickened broth mixture; cook over medium heat, stirring constantly, until thickened and bubbly. Transfer ducklings to serving platter; pour sauce over top. Garnish with orange slices and watercress, if desired.
Note: Seville oranges provide the bitter flavor characteristic of a Bigarade Sauce; however, another variety of orange may be substituted.