Combine honey, apple cider, water, lemon juice, and cinnamon stick in a saucepan; bring to a boil. Lower heat to medium and simmer, stirring frequently, until smooth, about 5 minutes. Add pears and cranberries and return to a boil; reduce heat to medium and simmer until sauce is thickened, 12 to 15 minutes. Refrigerate until chilled and flavors have blended, at least 2 hours.
