The nation of 4.8 million is the final stop on the couple's busy 16-day tour of Australia and the Pacific.
The Duchess of Sussex on Sunday congratulated New Zealand on becoming the first country in the world to allow women to vote 125 years ago, and said that effort had paved the way for others around the world.
She praised the tiara for being "so clean and simple", which she said was the ideal complement for her Givenchy wedding dress.
They were greeted at the airport by Prime Minister Jacinda Arden, having flown in from Australia with the Kiwi Invictus team.
Earlier in the day, the couple had received a traditional welcome to New Zealand when they rubbed noses with Maori elders on the grounds of Government House.
While Harry and Meghan have struck up plenty of new friendships during their visit, the prince was also thrilled to catch up with 98-year-old war widow Daphne Dunne, whom the prince struck up a friendship with during his last two trips to Sydney.
The Duke and Duchess of Sussex meet New Zealand Prime Minister Jacinda Ardern
Prince Harry and Meghan will touch down in Wellington about 3pm and will be officially welcomed at Government House by the Governor-General, Dame Patsy Reddy.
Harry returned the compliment, saying he and Meghan "genuinely couldn't think of a better place to announce the upcoming baby, be it a boy or a girl".
They will also visit Auckland and Abel Tasman National Park.
He said: "They are men and women who have confronted a challenge and overcome it".
A Government House representative later said it was a false alarm caused by a vegetable steamer in the kitchen.
They will take part in a wreath laying ceremony at the Pukeahu National War Memorial at the tomb of the unknown warrior at about 4:45pm. The games give sick and injured military personnel and veterans the opportunity to compete in sports such as wheelchair basketball.
The tune left Meghan, who is about four months pregnant and has taken medical advice about the Zika virus, in irrepressible giggles.More news: Florida Man Charged in Bombs Mailed to Trump Critics