You can contact Celebrity Cruises customer service by calling their toll-free number at 1-800-950-4401 / 1-888-751-7804 (U.S. and Canada) or +1-316-554-5961 (international). Their customer support is available daily to assist with bookings, cancellations, and general inquiries. You can also reach them via their live chat on the official website or email through their contact form.