Put water in saucepan, bring to a boil over medium high heat, then stir in sugar; turn heat down and simmer for 3 minutes.
Stir in the rum and simmer for 2 minutes more.
Remove saucepan from heat and let cool for a few minutes; then add the lime juice and lime zest, stirring to combine; set aside.
Using a melon-baller if you have one, cut melons into balls. If you don’t have one, just dice fruit into bite size cubes.
Put the melons into a big bowl, add blueberries, drizzle the sugar/rum mixture over the fruit and toss to combine well, being careful not to break up the melon pieces.
Cover bowl with plastic food wrap and put in refrigerator to chill until ready to serve.