Wash the cranberries and discard any rotten or wrinkled ones.
Combine the juices, honey and cinnamon stick in a 2 quart saucepan over medium-high heat. Bring to a boil and then reduce the heat to medium-low and simmer for 5 minutes. Add the cranberries and cook for 5 minutes. Add Kumquats and cook for another 10 minutes. Do not cook for more than 15 minutes total or the pectin will break down and your cranberries will not set.
Remove from heat and allow to cool for 5 minutes.
Remove cinnamon stick and spoon into a decorative mold. Refrigerate for at least 6 hours to allow it to fully set.
Remove from the refrigerator , overturn the mold and slide out the sauce.