Combine the cider, wine, cinnamon sticks, allspice berries, anise and cloves in a pot or dutch oven. Add the lemon zest, clementine zest, clementine juice and simple syrup.
Heat over medium high heat until the mixture just starts to boil. Reduce heat to a simmer and place the lid on the pot so it's slightly askew. Simmer for 10 minutes. Remove the cinnamon sticks and star anise and set aside.
Place a fine mesh strainer over a bowl and ladle or pour the grögg mixture through the strainer.
Wash and dry the pot that you simmered the Grögg in. Add the cider mixture back to the pot, along with the reserved cinnamon and star anise.
Just before serving, warm the Grögg over medium high heat. Remove from heat and stir in the rum. Cover tightly with the lid to keep the punch hot without cooking off the rum.
Ladle into cups and garnish with extra cinnamon sticks, star anise and orange peel for a festive feel.