In a medium saucepan, combine the juice, cinnamon stick, and cloves and bring to a boil. Reduce the heat and simmer.
Meanwhile, in a small saucepan, combine the cranberries, sugar, ground cinnamon, and 2 tablespoons of water and heat over medium-low heat, gently stirring, until the cranberries pop and are well coated with the sugar mixture.
When cool enough to handle, thread 3 to 4 berries each on 4 decorative toothpicks or skewers. Pour the mulled cranberry juice among 4 mugs and garnish with the cranberry swizzle.