In a small bowl combine the water and sugar and stir until dissolved.
In the carafe of a blender, combine the watermelon, raspberries, lime zest, lime juice and 3 tablespoons of the sugar water. Cover and blend or process until smooth.
Pour the watermelon mixture through a fine mesh sieve pressing lightly with the back of a spoon. Discard any pulp and seeds. Divide the watermelon mixture between 6 popsicle molds. Place the popsicles in the freezer for 60 minutes.
In the meantime, rinse out the blender carafe. Add the honeydew melon and any remaining sugar water to the blender. Process until smooth. Pour the honeydew into a small measuring cup with a spout and refrigerate until the watermelon portion is thick and slushy.
Divide the honeydew puree between the 6 popsicle molds on top of the watermelon mixture. Return to the freezer for 45-60 minutes. Remove the popsicles from the freezer and insert sticks into the molds. Freeze overnight or until firm.
To remove from the molds, dip the bottoms of the popsicles in warm water for about 15 seconds. Try to remove the popsicles from the mold. If they will not come out, dip in warm water again for 15 seconds and repeat as needed.
Store popsicles in an airtight container in the freezer.