Bring apple juice, honey and sugar to boil in a medium saucepan over medium heat. Wash and rinse the cranberries in cold water. Add cranberries and return to boil. Reduce heat and boil gently for 10 minutes, stirring occasionally. Pour into a bowl through a strainer, using the back of a spoon to smash the cranberries through the strainer. Scrape as much sauce from the bottom of the strainer as possible, and continue pouring and snagging until you have processed the entire pan.

Cool completely at room temperature. Refrigerate until serving.