Place the orange and lime zest in the bottom of large, wide saucepan.
Combine the orange juice, lime juice, and water in a medium bowl or large measuring cup.
As you peel and dice up the apples and pears, place the chunks in the citrus-y water to prevent discoloration.
When you have finished placing all the chopped apples and pears in the liquid, transfer everything to the large saucepan. Add the dried apricot halves and dried cherries. Stir in the honey.
Bring the fruit mixture to a boil over high heat, stirring occasionally.
Cover the pot, lower the heat to simmer, and cook for 10 minutes, stirring once halfway through the cooking time.
Transfer the warm fruit compote to a serving or storage container. Cool to room temperature. Cover and refrigerate overnight.
Serve the chilled compote in dessert dishes.