Microwave bourbon (or rum) and brown sugar in a microwave-safe dish until hot, about 1 minute. (Alternatively, heat in a small saucepan over medium heat, stirring occasionally, until hot.) Stir until the sugar is dissolved. Pack cherries into a small jar and pour the hot liquid over them; gently press on the cherries to make sure they are submerged. Cover and refrigerate for at least 1 week or up to 1 month.