Line a baking sheet with parchment paper and grease with oil. Heat sugar with 4 tablespoons of water in a saucepan and let caramelize light yellow over high heat while stirring. Stir in the sesame seeds and continue caramelizing until golden brown. Then spread this mixture on the baking sheet and let it cool down.
Cut the melon and pineapple into bite-sized pieces. Mix the rum with honey and lemon juice and mix the marinade with the fruit. Let it steep for a few minutes.
Finely chop the sesame brittle or serve as a brittle place with a fruit salad.