In 3-quart saucepan or Dutch oven, cook cinnamon stick, cloves and ginger over medium heat 2 to 3 minutes, stirring constantly, until cinnamon is fragrant.
Gradually stir in juices. Heat to boiling over medium-high heat; reduce heat to medium-low. Simmer uncovered 15 minutes.
Press mixture through fine-mesh strainer into heatproof pitcher; discard spices. Serve warm. Garnish with pineapple and orange twists.