Preheat oven to 180 degrees C. Lightly grease two 12-hole muffin tins.
Spoon the mincemeat into a large bowl then stir in the marzipan, orange zest and rum.
Lay out the puff pastry on a lightly floured surface. Cut out 24 circles using a round pastry cutter or a glass. Place the circles into the prepared muffin tins, and press gently into the base and sides. Add a spoonful of mincemeat into each one, being careful not to overfill, as the filling might bubble out of the pastry.
Bake in the preheated oven for 15 to 20 minutes, or until pastry is golden. Remove from the oven and set aside to cool for a few minutes then transfer to a wire rack. Serve warm.