In a cocktail shaker or large glass, muddle together the fresh cherries and lime juice.
Next, fill 2 good sized tumbler glasses (or one very large glass, if a single serving) with ice, and place a small sieve on top.
Strain the lime & cherry mix into the glass, and discard the cherry remnants. (We tried keeping them, but they always plug up the straw, and make drinking a challenge.)
Now, add the cherry simple syrup and top with the club soda.
Stir gently, and garnish with a lime round or a cherry.
This drink benefits from resting for a few minutes before enjoying.