Combine cherries (pits and all) and sugar in a medium saucepan over medium heat. Stir to coat the cherries in sugar than use a potato masher to squash the cherries and release their juice (this will be easier to do once they warm up a little bit).

Bring to a simmer, stirring occasionally, until the sugar has dissolved. Keep at a simmer, adjusting heat as necessary, and cook until cherries are soft and start to break down, about 15 minutes.

Set a strainer over a bowl and pour cherry mixture into the strainer. Press down on the solids until all the juice has gone through the strainer. Discard solids and chill syrup until ready to use.

When ready to serve, combine soda, lime juice, and syrup in a large pitcher. Stir gently to combine. Fill pitcher with ice and stir in lime slices. Taste and add more lime juice if it is too sweet. Serve immediately in ice filled glasses.