Heat oven to 175 degrees. Puree pineapple and mango with 1 Tbsp honey or persimmons with 2 Tbsp honey in a food processor until smooth.
Spread puree on a Silpator parchment-lined baking sheet in a thin, even layer about 1/8-inch thick. Tap baking sheet on the counter a few times to release air.
Bake until set in the middle and barely tacky, 2 1/2 to 4 hours. Let cool completely, then use a pizza cutter to slice into 2-inch-wide strips. Halve each strip crosswise and roll in parchment strips of equal size.
Fruit leathers can be stored in an airtight container up to one week.