It depends which credit card; often the links to overseas card authorizations are down so whether a charge is approved depends on your specific card. I have a dozen different cards for travel because of this problem, and there are some that fail 90% of the time. Other work 100%. NZ was one of the first countries to roll out a nationwide EFTPOS network so it is found in very small and isolated towns -- much more so than in the US or Canada, but your problem might be in credit/debit card acceptance presuming you don't have a NZ issued card.