Share your experience!
Are you using the correct SIM card size or did you trimmed/cut a regular SIM card? how old is the SIM card?
I've seen users with a similar issue when they insert the SIM card backwards, which will damage the phone. You could repair the phone with PCC
Bridge (for Mac)
Alternatives on How to backup Xperias
http://talk.sonymobile.com/thread/36355
Sir, i had the same problem and i found a solution today itself.
Step1: go to setting > mobile networks> select the preferred network type for that sim which is working. I did to LTE though sim was GSM. And select the preferred network type to GSM for non working sim.
STEP2 : then interchange the preferred network types and you will see that, your sim will work as previous.