It's easy to freak out if you're staring at the phone waiting for it to do something. So, first take a deep breath and a calm down. First, double check that you do have the right time and day just in case (you're probably fine, but it happens). Then, take a moment and put things in perspective. It's not that they changed their minds or don't want to talk to you. When you interview in person someone is usually there to tell them that someone had arrived for an appointment and to give them some warning to wrap up whatever they are working on. That doesn't happen when the appointment is for a phone call so it's easy for someone to lose track of time in the midst of work or get backed up. That is most likely what is happening.
It can be hard to wait patiently but give it about 15 minutes before you do anything. Then, put together a brief, professional message and give them a call - preferably from another phone or at least one with call waiting so you don't miss an incoming call while you are trying to check in. You can say something like "I just wanted to check in and see if you're still available or if it would be better for you to talk another time. Thank you." Don't make accusations or say anything implying the person is wasting your time. Be cheerful, positive, and understanding. Everyone is busy.
If you still haven't heard anything back by the next day, send an email to follow up and ask about rescheduling. Again, be positive and don't try to place blame because if they missed the day of the interview entirely without contacting you it's likely something unexpected happened that requires their immediate attention. It's not personal, but acting like it is will leave a bad impression.
There is one other thing worth mentioning though when it comes to scheduling phone interviews: sometimes miscommunication can cause issues. So when you schedule your interview, be clear about who will actually make the call and what number should be used. If your interviewer is in another time zone, be sure to clarify the time difference and ensure that everyone is on the same page. These small details can get overlooked and cause a lot of stress later so deal with them up front to avoid any confusion.
Have you ever found yourself waiting for a late call from a phone interviewer? How did you handle it? Share your thoughts in the comments.