1In 1-quart saucepan, heat cranberry juice cocktail and sugar to boiling over medium-high heat. Add cinnamon stick, gingerroot, cloves and anise. Reduce heat to low; simmer uncovered 15 minutes.
2Into heatproof pitcher, strain mixture through fine-mesh strainer; discard spices. Stir rum and liqueur into pitcher. Pour cocktail into mugs. Garnish with cranberries, orange slices and additional cinnamon sticks and star anise.