How do I transfer the cellular service from one iPad to another? I have a first-generation iPad mini with Verizon LTE service and I’m replacing it with a second-generation mini. What do I need to do to “transfer” the cellular service from the one to the other? (In other words, I want the new device to seamlessly replace the old one as far as the carrier is concerned.)

Is it a simple matter of moving the old SIM card to the new device, or do I need to get the carrier involved?
I've always involved the carrier, but I don't know if you have to involve VZW in the switch.

If you have a shared data plan, then you will certainly want to get them involved to ensure you don't make a stand alone plan when the old SIM hits the new device. I've had no issues with exchanging a device and not had to pay the fee for enrolling the new device since it simply replaced the old one.

If you are on a month to month plan and don't mind re-paying the activation charge, you could simply set up the new device and let the old device's plan expire.

Much depends on if you use the device to set up the account or want to have verizon enter the details into their system as the different types of accounts have different manners of adding the new device to the plan.