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The Air New Zealand has Air New Zealand Airpoints Platinum Mastercard that is not available for application for the US citizens. Their card earns reward Airpoints per New Zealand dollars. If you want to earn rewards on New Zealand Airlines, as an everyday card I would choose Discover it® Miles, which gives you 1.5 miles on all purchases. You'll be able to use it for travel and, in addition, Discover matches first-year miles at the end of the year (provided you are a new cardmember) – solid reward by itself.