Meanwhile, slice the orange.
Line a sieve with a coffee filter or a double layer of cheesecloth. Put the sieve over a medium sized bowl. Pour the hot cranberry juice through the sieve and into the bowl.
Rinse out the saucepan and pour the warmed juice back in. Cook over medium heat until it simmers. Drizzle in the orange liqueur My preference is Cointreau, but you could also use Triple Sec or Grand Marnier. Stir.