Peel pears, leaving stems intact. Slice 1 inch from top of each pear to form a cap. Slice about 1/4 inch from base of each pear so it will sit flat. Core each pear. Rub outside of pears with cut sides of lemon halves. Discard lemon.
Combine cranberries, 1/2 cup sugar, crystallized ginger, and rind in a food processor; pulse until finely chopped. Place pears in a 13 x 9-inch baking dish. Fill each pear cavity with 3 teaspoons cranberry mixture, 1 teaspoon at a time. Top each pear with its cap. Pour cider over pears.
Drizzle butter evenly over pears. Combine 1 tablespoon of sugar and ground ginger; sprinkle evenly over pears. Carefully cover with foil. Bake at 400° for 1 hour or until tender, basting every 20 minutes.
Using a spatula, carefully remove pears from baking dish; place on individual dessert plates. Pour liquid from baking dish into a medium saucepan. Cook over medium-high heat until reduced to 1/2 cup (about 12 minutes). Drizzle 1 tablespoon sauce over each pear.