1. Cut the melons in half across the middle.
2. Scrape out the seeds and discard.
3. Using a melon baler, scoop out 20-24 balls and set aside for the garnish.
4. Scoop out the remaining flesh and place in a blender or food processor.
5. Place the sugar, water and lime zest in a small pan over a low heat.
6. Stir until dissolved, bring to a boil and simmer for 2-3 minutes.
7. Remove from the heat and leave to cool slightly.
8. Pour half the mixture into the blender or food processor with the melon flesh.
9. Blend until smooth, adding the remaining syrup and limejuice to taste.
10. Pour the mixture into a bowl, stir in the basil and chill.
11. Serve garnished with basil leaves and melon balls.
12. Add the syrup in two stages, as the amount of sugar needed will depend on the sweetness of the melon.