Continental Airlines accepts a variety of payment methods for booking flights and managing reservations. Typically, customers can use major credit cards such as Visa, MasterCard, American Express, and Discover. Debit cards that are linked to these networks are also generally accepted. In addition to credit and debit cards, customers may also have the option to use travel vouchers or certain forms of electronic payment like PayPal, depending on the specific transaction and the region. It is always advisable to check the most current payment options available on the official Continental Airlines website, as these can vary or change over time. Additionally, customers should ensure that their chosen payment method meets any required criteria, such as having sufficient funds or being within the expiration date.