1. Halve melons and scoop seeds into a sieve set over a bowl. Let juice drip into bowl, then discard seeds.
2. Working over the bowl, scoop the melon into neat balls with a melon ball scoop, letting juices fall into bowl with the melon balls.
3. Add sugar and salt and stir gently to combine.
4. Peel peaches, halve and slice into a bowl containing the lemon juice. As each peach is added to bowl, stir gently to coat it with lemon juice to prevent discoloration.
5. When all are prepared, add peach slices and lemon juice to bowl of melon balls. Stir gently, add rose water to taste, amount depending on strength of rose water used. Cover bowl and chill for several hours.
6. To serve, pile into individual dessert glasses, top with a little shaved or crushed ice and serve immediately.