Halve the melon, remove the seeds. Cut off 2 thin slices to decorate. Peel the rest of the melon, chop roughly and put into a blender. Add yoghurt and honey and puree. Wash lemon balm, shake dry and, except for something to garnish, pluck off leaves and cut into strips.
Fold the lime zest and lemon balm into the drink. Pour the drink into 4 glasses and garnish with halved melon and lime slices and lemon balm.