Prepare a boiling water bath canner and 6 half-pint jars.
In a large, non-reactive pot, combine the cherries, sugar, lemon zest and juice, and rosemary sprigs.
Give the contents of the pot a good stir and let it macerate off the heat for about an hour.
When you’re ready to cook, put the pot on the stove over high heat and bring to a boil. Once it starts to roll, reduce the heat to medium-high.
Cook for 15 to 20 minutes, stirring regularly, until the liquid in the pot thickens and the cherries soften.
Remove the pot from the heat and fish out the rosemary stems. Ladle the compote into the prepared jars. Wipe the rim, apply the lid and band, and process in a boiling water bath for 10 minutes.
When the time is up, remove the lid from the pot and turn off the heat. Let the jars rest in the cooling water for five minutes. When that time is up, remove jars and set them on a folded kitchen towel to cool.
When the jars have cooled enough that you can comfortably handle them, check the seals. Sealed jars can be stored at room temperature for up to a year. Any unsealed jars should be refrigerated and used promptly.
