Rinse lemon balm under running water to clean. Stir together all 3 ingredients in a medium saucepan over medium-high heat. Using a spoon, gently smash them against the sides of the pot to release the flavor.
Remove from heat, and let stand 30 minutes. Pour liquid through a wire-mesh strainer into an airtight container or Mason jar, discarding lemon balm leaves. Cover and chill 4 hours. Syrup may be stored in refrigerator up to 1 month or poured into a plastic freezer container or an ice cube tray and kept frozen for up to one year.