I've had the iphone 5 for about 6 months now. For the past few weeks, I've gotten the "No SIM Card Installed" message. I would shut the phone off and restart to get service back. This would happen several times a day. Eventually I restored the phone to factory settings. Only 2 days later, I kept getting the same message again. Yesterday, I went to a verizon store to have the SIM card replaced. Today, the very next day (less than 24 hrs), I'm getting the error message again. I'll probably go back to the verizon store again today, but I don't want this to be a re-occurring issue. Is it the phone itself that is damaged?
I had the same problem. Apple support suggested a reset by pressing both the home button and the sleep/wake button.
When the Apple logo appears, you can release the buttons. Then the lock screen appears with Verizon at the top instead of "no sim". This seems to have fixed it.