Preheat the oven to 350 degrees F. Line a 12-cup muffin tin with paper liners.
Pulse the pistachios, flour, baking powder and salt in a food processor until finely ground.
Whisk the confectioners' sugar and eggs in a large bowl, then whisk in the pistachio mixture until just combined. Stir in the melted butter until just incorporated.
Spoon 2 tablespoons batter into each muffin cup. Bake until slightly puffed and just beginning to set, about 8 minutes. Place 1 or 2 cherries in the center of each cake and continue baking until the cakes feel springy and the edges are lightly browned, 10 to 12 more minutes. Transfer to a rack and let cool 10 minutes in the pan, then remove from the pan to cool completely. Dust with confectioners' sugar.