Combine water and granulated sugar in a small saucepan. Heat over medium heat, stirring occasionally, until the sugar is completely dissolved. Bring to a gentle simmer, then remove from heat and let cool completely. This can be made ahead and chilled.

If using fresh cherries, ensure they are pitted. If using frozen, allow them to thaw slightly for easier blending. In a blender, combine the cooled simple syrup, pitted cherries, fresh lime juice, lime zest, and optional salt and food coloring. Blend until completely smooth.

Pour the cherry limeade mixture through a fine-mesh sieve into a large bowl, pressing down on the solids with a spatula to extract as much liquid as possible. Discard the pulp. This step ensures a super smooth sorbet texture.

Cover the bowl and refrigerate the sorbet mixture for at least 2-4 hours, or preferably overnight, until it is thoroughly chilled (ideally below 40°F / 4°C). This is crucial for optimal churning.

Once the mixture is well chilled, pour it into your ice cream maker and churn according to the manufacturer's instructions. This typically takes 20-30 minutes, or until the sorbet has the consistency of soft-serve ice cream.

Transfer the churned sorbet to an airtight freezer-safe container. Press a piece of parchment paper or plastic wrap directly onto the surface of the sorbet to prevent ice crystals from forming, then seal the container. Freeze for at least 4 hours, or until firm, before serving.