In a medium saucepan on medium-low heat, add the cherries, sugar, and lime juice. Allow to warm for several minutes, then begin to gently smash the cherries with a potato masher. Continue gently smashing until all the cherries are thoroughly mashed. Remove from heat.
Set a mesh strainer over a large bowl and pour the cherry lime mixture into it. Use the potato masher to press the mixture down onto the strainer, releasing any last juice remaining in the cherries. Discard the skins and pits, then place the syrup in the fridge to cool.
In two small bowls, add ½ cup of the tapioca to each, then pour 3 tablespoons of the cherry lime syrup on top of each. Stir until thoroughly mixed, top with an extra drizzle of syrup and some fresh lime zest for garnish. Enjoy!