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The best phone number to call Southwest Airlines is listed below, along with tips on how to avoid phone lines and speak with a representative right away. Southwest Airlines' best phone number is this one because users like you used it in the previous 18 months and provided feedback. The department in charge of handling calls frequently handles customer service challenges such reservation changes, questions about reservations, flight consultations, special requests, cargo refunds, and other issues related to customer service. According to customers, the Southwest Airlines call center you are calling from employs Texans and is open twenty-four hours a day.