Preheat the oven to 400 degrees F.
In a small saucepan, heat the orange and lemon juices with 1/2 cup of the port. Add the zest and cook until tender, about 10 minutes. Reserve.
In a medium saucepan, combine the cranberries, onion, 2 cups port, ginger, brown sugar, salt, pepper, and cinnamon. Over medium-high heat, cook until the relish thickens, 15 to 20 minutes, stirring occasionally. Stir in the remaining 1/2 cup port, the orange liqueur, and the reserved orange and lemon juice and zest mixture. Set aside.
Cut off the top 1/4-inch of each apple. Using a melon baller, remove the core of the apple, being careful not to pierce the sides or bottom of the apples, to make apple "cups". Place the apple cups in a small baking dish. Spoon the cranberry relish into the apples. Spoon the excess relish around the apples. Cover with foil and bake until apples are tender, about 30 to 45 minutes.
Recipe adapted from Adventures in the Kitchen by Wolfgang Puck, Random House, 1991