Combine water and sugar in a medium size pot. Cook over medium-low heat until the sugar completely dissolves.
Add lemon zest, juice, and cherries. Cook for 5 minutes. Use an immersion blender or pour mixture into blender and puree until smooth.
If you are using an ice cream maker, pour the mixture into a bowl, cover, and refrigerate for 2 hours or overnight. Once cold, pour the sorbet mixture into bowl of ice cream maker and churn according to manual.
If you aren't using an ice cream maker, pour the sorbet mixture into a metal loaf pan. Cover and freeze at least 4 hours or until completely solid.