Put the ginger, lime zest and caster sugar in a pan with 600ml (1 pt) water. Bring to the boil, then reduce the heat and simmer for 20 minutes, until syrupy. Stir in the lime juice, then strain the liquid through a sieve into a sterilized bottle and leave to cool. Chill until needed.
To serve, pour a little cordial into a glass, then add a handful of ice cubes, a sprig of mint and top up with sparkling water.