Process cantaloupe, vinegar, salt, and 1/2 cup water in a blender until smooth.
Combine sugar, honey, and remaining 1/4 cup water in a saucepan over medium; cook, stirring constantly, until sugar is dissolved, 2 to 4 minutes. Remove from heat, and cool 10 minutes.
Stir together cantaloupe mixture and honey mixture in a medium bowl until combined. Cover and chill until cold, about 30 minutes.
Pour mixture into freezer bowl of a 1-quart electric ice-cream maker, and proceed according to manufacturer's instructions. (Instructions and times will vary.) Transfer to a freezer-safe container, and freeze until easily scooped, at least 4 hours.