You can get a local SIM in New Zealand or use Verizon's roaming plan for $40.
You can use the iPhone 6 4G LTE 16GB Space Gray for voice, text and data in all selected countries. Before you travel, contact Verizon Wireless by dialing *611 from your wireless device or (800)922-0204 from any phone to enable international roaming. I would not use free buy as you since this is risky for a big unintended bill in the thousands
Get UNLIMITED access to select Global Wi-Fi hot-spots with Verizon Wi-Fi Connect when you add a Global data bundle to a line on your account.
Many Phones, allow the international call prefix "+" to be entered in their saved number lists, often by holding down the '0' key or with two consecutive presses of the * key. When making a call the system then automatically converts the "+" to the correct international prefix.
Dial Plus Sign then 1 then ten digit U.S. number
Dial Plus Sign then Country Code then Local Number with Area Code (if applicable)
Dial Plus Sign then Country Code then international number
Dial Plus Sign then 1 then 908-559-4899
New Zealand (64 - None)
Dial 00 800-50050099
Trouble with your device? If you cannot place a call from your VZW device, please call Global Support from any landline phone using the dialing instructions above in the "Customer Service from a landline" section.
The VZW Global Roaming Hotline will then prompt you to enter your 10-digit mobile number.