Puree 2 cups pitted cherries in a food processor. Push the puree through a fine mesh strainer into a large glass measuring cup. Discard any remaining solids.
Add the lemon juice to the cherry juice and stir to combine.
In a large glass measuring cup or bowl, stir together yogurt and honey. Add about half the yogurt mixture to the cherry juice and stir to combine.
Pour a small amount of the cherry mixture into 10 popsicle molds. Divide the honey yogurt evenly amongst the molds, then top with the remaining cherry mixture, being sure to leave a small space at the top.
Push one or two cherry halves into each popsicle mold, cover, and insert wooden sticks. Allow to freeze until firm, about 4 hours.
To easily remove popsicles from their mold, remove from the freezer and run under hot water for a few seconds.