Calling does very little*

If you know you are not going to make the flight and call 10+ minutes before departure, all you can do is cancel your booking for a credit or pay the difference in CURRENT fare to change to a later or next day flight.
*exception is if the flight already has a posted 20+ minute delay, then you can call for a free same day change.

If you already missed it, calling is useless -- they will tell you that you lost/forefit your $.

As others posted above, only if you make it to the airport agent within 2hrs of departure, an option unavailable and undisclosed on the phone suddenly appears. They can preserve the value of your ticket by allowing you to standby for the next flight.. (if you don't clear standby, you will stay on standby for the next flights and even next days until you do).

/reason #450 that I am adverse to cruises: years ago I learned that disembarking a cruise ship can happen several HOURS(!) after arrival time. My wife and her family got off a ship in Seattle. From 2000 miles away, I had to convince them that first guy they saw standing next to the 60 minute cab line was a gypsy limo driver that they needed to hire at any cost. Once at the airport I askef them to choose between cut everyone in the 30 minute TSA line and begging forgiveness or standing in the terminal and watching the last flight with space for 2 days take off without them.