My iPhone 5s has been stuck on "searching all day. My voicemail says that I don't have a sim card
Try removing, then reinserting the SIM card; that may get the connection re-established.
SIM cards can go bad, so you may need to get a new one at a Verizon store (they are free) or by calling CS to have one mailed to you.
I do appreciate your suggestion SuzyQ. Willpeet, have you tried what was suggested? Are you still having the issue? Does it get better if you travel to a different area? AmberF_VZWFollow us on Twitter @VZWSupportIf my response answered your question please click the "Correct Answer" button under my response. This ensures others can benefit from our conversation. Thanks in advance for your help with this!!