Swiss Airlines return procedure is simple. Request a refund online if you are less than 24 hours away from your flight. Dial Swiss Airlines Phone Number at +1-877-818-6735 or UK +44 800 368 6377 for refund status. They can be reached via the official phone number shown above. You can communicate your concerns to them by email, live chat, social media profiles, or by meeting them in person at the airport.