Wash the cherries thoroughly and pit them, then halve each one. In a blender, combine the pitted and halved cherries with the water, cane sugar, freshly squeezed lime juice, salt, and vanilla extract. Blend on high speed until you achieve a completely smooth puree with no cherry chunks remaining. I like to taste the mixture at this point and adjust the lime juice or sugar if needed—the tartness of the lime should complement the sweetness of the cherries without overpowering them.
Pour the cherry puree from Step 1 evenly into popsicle molds, filling each cavity to just below the rim. Insert popsicle sticks into the center of each mold, positioning them so they stand upright and won't tip over during freezing. I recommend using molds with built-in stick holders if you have them, as they keep the sticks perfectly centered and prevent them from shifting.
Place the filled molds in the freezer and freeze for at least 6 hours, though overnight (8-12 hours) is ideal for completely solid popsicles. The longer freezing time ensures the popsicles are firm enough to handle without breaking apart.
Remove the molds from the freezer and run the outside of each mold under warm (not hot) running water for 30-45 seconds, gently wiggling the sticks as you do. This warms the outer edges of the puree just enough to release it from the mold without melting the inside. Gently push up from the bottom of each mold or pull on the stick to release the popsicle, then serve immediately.