Contacts are stored in the phone's memory. Unless a Verizon phone is a "Global" or "World" phone, it doesn't use a SIM (and none of the "Global" phones roam on GSM in the US, either).
You can backup the contacts using the (free if you have MyAccount @ vzw.com) backup assistant program. If you want to backup locally, you c an use BitPim and a cable/bt to backup to your PC.