In a large saucepan combine apple cider, apricot nectar, and brown sugar. Cut a double thickness of 100-percent-cotton cheesecloth into an 8-inch square. Combine cinnamon and cloves on center of cheesecloth. Bring up corners of cheesecloth and tie with cotton string. Add to saucepan. Bring mixture to boiling; reduce heat. Simmer, covered, for 10 minutes.
Remove and discard spices. Serve warm. Garnish with caramel-flavored candy stick, if desired.