This dessert is best with sweet, almost too-ripe melon, as food loses a bit of its sweetness when frozen. It's an acceptable tradeoff, because the frozen melon balls are refreshingly cool and are like a sorbet as made by Mother Nature herself. Just about any musk-type melon (those with web-like markings on their skin, such as canary or honeydew) can substitute for cantaloupe--a combination of two or three is tastes and looks terrific, if you have a selection on hand. Don't use vintage port for the syrup--a modest California brand is fine.
2. Bring the port and brown sugar to a boil in a medium saucepan over high heat. Cook until the mixture is syrupy and reduced to 3/4 cup. Transfer to medium bowl set in a larger bowl of ice water. Let stand until the syrup is cool, about 20 minutes. Cover and refrigerate the syrup until ready to serve.
3. Divide the frozen melon balls among 6 wine glasses and top each with 2 tablespoons of the syrup. Garnish with mint sprigs and serve immediately.