All arrivals from the United States and United Kingdom are now required to provide a negative result 72 hours before departure.
A Customs spokesperson told RNZ that a person was leaving the UK under an "emergency situation" and received a warning instead of a fine.
The spokesperson said Customs is currently taking an "educational approach" to people arriving without evidence of a pre-departure tests.
From January 29, fines of up to $1000 can be issued for arriving without a negative test.
Soon travellers from nearly all countries will have to provide a negative Covid-19 test before arriving in New Zealand under tough new rules announced on Tuesday.
Covid-19 Recovery Minister Chris Hipkins said he had authorised the Director-General of Health to roll-out the requirement to cover all countries apart from Australia, Antarctica and some Pacific nations.
"New Zealand already has some of the most stringent border protection measures in the world. Today's amendments further strengthen that position in line with the Government's overall elimination strategy," Hipkins said.
Children under 2 will be exempt from the pre-departure test, as will travellers who can provide a medical certificate showing they have recovered from a past case of Covid-19 and are considered no longer infectious.
Hipkins said the 72-hour time period for testing could be extended for another 24 hours if a person's flight was delayed or cancelled, or test results were not returned in time.
Passengers arriving from any of those countries will also now have to undergo a Covid-19 test on their first day in the country.