In a small saucepan, stir together the sugar and ⅓ cup water and bring to a simmer. Simmer and stir until the sugar has completely dissolved, then remove from the heat and allow to cool.
Meanwhile, blend the cherries, salt, and ⅓ cup water in a food processor or blender until smooth. Pour through a fine mesh sieve into a clean bowl, and use a spoon to stir and squeeze out as much liquid as possible. Stir in the lime juice and lime zest. When cooled, stir in the sugar syrup.
Pour into a wide and shallow dish (I used a 9” glass pie pan. Liquid should be no deeper than 1”)
Cover and freeze. After 1 hour, remove from the freezer and use a fork to scrape and mix up the ice. Repeat every 1-2 hours for 5 hrs. When the granita is finished, it can be transferred to an airtight container and stored for up to 3 months.