Rinse, peel, and core pears; cut into about 1/2-inch cubes. Grate enough peel (orange part only) from orange to make 1 1/2 teaspoons. Ream juice from orange; measure, and add enough water to make 1/2 cup.
In a 3- to 4-quart pan over high heat, stir orange juice mixture, grated peel, sugar, star anise, and cinnamon stick until sugar is dissolved, 1 to 2 minutes. Stir in honey and pears and bring to a boil; reduce heat to medium and stir occasionally until edges of pears are barely tender to bite, about 3 minutes.
Stir in cranberries. Cook, stirring occasionally, until cranberries begin to pop and pears are tender when pierced, 6 to 8 minutes.
