Rinse the mint, pat dry and pluck the leaves from the stems. Wash the limes with hot water, dry them and cut them in half. Squeeze the juice from half a lime and set aside.
Cut the remaining lime halves into pieces or slices and distribute them in the glasses. Add ice cubes or crushed ice. Put the elderflower syrup in a mug, add the squeezed lime juice, mix the two well. Distribute the syrup and mint evenly in the glasses and fill everything up with mineral water and ginger ale.