Whirl melon in a blender or food processor until smooth. Pour into a bowl, cover, and chill until cold.
In a small saucepan, bring herbs, if using, and 1/2 cup water to a boil. Remove from heat and stir in honey. Pour into a bowl and chill until cool. Strain into melon purée.
Freeze in an ice cream maker according to manufacturer's directions. Serve immediately.
Note: Nutritional analysis is per 1/2-cup serving.