Place a small plate in the freezer to test the jam later.
Chop about 3/4 of the pitted cherries in half or quarters and leave the remaining 1/4 whole.
Place the cherries in a large non-reactive pan with 2 tablespoons of water. Add the lemon zest and juice and gently mash. Heat over medium low, stirring occasionally, until cherries are very soft, about 15 to 20 minutes.
Stir in the sugar and heat over high heat, stirring frequently, including scraping the bottom and sides of the pan. Bring to a roiling boil for about 10 minutes, continuing to stir, until bubbles start to subside and mixture thickens.
When mixture starts to gel and will coat the back of a spoon, remove from heat. Dribble some jam onto the frozen plate and return to the freezer for a couple of minutes. Remove the plate and gently push against the jam with your finger. If it wrinkles it’s ready. If it doesn’t wrinkle, return to heat for another 5 minutes and test again.
Ladle jam into clean glass jam jars, cover and let cool at room temperature, then store in the refrigerator.