Muddle the cherries and lime wedges in a mixing tin. Add the gin, Simple Syrup, bitters and ice and shake. Pour the contents into a glass and top with club soda.
Combine the sugar and 1 cup water in a small saucepan and bring to a boil. Cook, stirring, until the sugar dissolves. Remove from the heat and let cool completely. Keep covered in the refrigerator up to 1 month.