Prepare martini glasses by filling them with ice, and cold water.
Working quickly to avoid a watery Manhattan, add your bourbon and sweet vermouth to a cocktail shaker with a handful of ice, and shake for several seconds. (If you don’t have a cocktail shaker, up a measuring cup with a spout, and stir mixture with the ice.)
Immediately empty out the water from the martini glasses, and divide Manhattan mixture evenly between them. Garnish with a cherry or orange peel.