Apple Watch 5
Will a USA Apple Watch work in New Zealand?
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A North American (Canada, U.S., Mexico, Puerto Rico) cellular model will Not!
A GPS only model works anywhere the paired iPhone works.
HOWEVER, the warranty is Not international, so you would have to return to the U.S. for warranty repairs.
Also the New Zealand government has not approved the ECG app, so that will not work on the Series 4 or 5 until it gets approval
Apple Watch ECG countries
https://www.apple.com/watchos/feature-availability/#branded-ecg