Put the cherries, blueberries and water in amedium-sized pot (taller sides are better since you'll be blending in the pot)and bring them to a boil. Simmer until the fruit begins to break down, about 10minutes. Puree the fruit, using an immersion blender or by pouring it into a blender and then back into the pot again. If you're using the oven, preheat it to 175°F. Line a jelly-roll pan or rimmed baking sheet with unbleached parchment paper or a Silpat and set aside.
Add the sugar and continue to simmer the fruit puree over low heat, stirring frequently, until it thickens to the consistency of baby food - this may take 10-15 minutes.
Spread the sweetened, thickened puree on to the baking sheet, tilting to create an even layer about 1/4-inch thick. The edges will dry out more quickly so try to leave them a tiny bit thicker.
If you're using the oven, bake until just tacky to the touch which can take anywhere from 3-6 hours, depending on how juicy your puree is. If you're using a food dehydrator, set it to 130° F and cook for between 6-12 hours, testing every hour or so until smooth to the touch with no visibly wet spots.
Cool to room temperature. Slide the parchment paper or Silpat onto a cutting board and peel the leather off. Then roll each sheet up and slice it into two- to three inch-wide pieces. Store rolled up in an airtight container on the counter for up to a month.