Cut the tangerines crosswise through the skins into 1/2-inch slices, then quarter the slices. In a small bowl, toss the tangerines with 1/2 cup of the sugar. Cover and refrigerate overnight.
In a heavy, medium saucepan, combine the candied tangerines and their liquid with the remaining 1/2 cup of sugar and the orange juice. Bring to a boil, then simmer over moderately low heat until the tangerine skins are soft and the liquid is syrupy, about 50 minutes. Add the cranberries and cook over moderately low heat until their skins just begin to split, about 15 minutes.
Drain the cranberries and tangerines in a colander set over a bowl and return the liquid to the saucepan. Boil the liquid over moderately high heat until syrupy, about 15 minutes. Pour the syrup over the fruit and let cool completely.
Make Ahead The sauce can be refrigerated for up to 1 week. Bring to room temperature before serving.
