Leftover artichokes can be saved in an air-tight container in the refrigerator. Drain the excess water from the artichokes and refrigerate for several days. To reheat them, microwave until warm or you can even grill them! To grill the artichokes, cut them in half length-wise, remove the choke, drizzle with a little olive oil, salt, and pepper, and then grill, flesh-side down, until hot.