Heat oven to 350°F (175°C). Line a 12-cup muffin pan with paper liners.
Whisk the flour, sugar, baking powder, baking soda, cinnamon, and fine salt in a large bowl.
In a second bowl, whisk eggs, oil, and vanilla. Fold in zucchini, then stir the wet mixture into the dry ingredients just until no flour streaks remain.
Fold in the chopped cherries. Divide batter among the cups, filling each about three-quarters full. Bake 18–22 minutes, until the tops spring back and a toothpick comes out clean. Cool in the pan for 5 minutes, then transfer to a rack.