Combine the bourbon, lemon juice, lime juice, and syrup. Fill a cocktail shaker halfway with ice, and fill two-thirds full with the cocktail mixture. Shake for 30 seconds and pour into martini glasses. Add a maraschino cherry and serve ice cold.
To make sugar syrup, combine 1 cup of sugar and 1 cup of water in a small saucepan and cook over medium heat until the sugar dissolves. Chill thoroughly before using.