If you are looking to make a reservation on Delta Airlines, the best way to do this is by using their online reservations system. The reservation number you will need is (716)351-6210. This number can be found on most Delta Airlines tickets and reservations. What is the 1-Reservations Number for Delta Airlines? Delta Airlines has a 1-Reservations Number that you can use to make reservations for flights, hotels, car rentals, and other travel-related services. The -Reservations Number is available on Delta's website, in its call centers, and at most airport ticket offices.