They are thankful they have travel insurance and will be in touch with the Danish embassy.
Ms Johnsen said they couldn't believe what was happening when the man drove off.
"I thought, 'this is not right, he's coming back or something'," she said.
"Then we kind of panicked, I suppose."
They reported the theft to the police and contacted a family they knew.
"We've had so many good experiences here in New Zealand," Ms Johnsen said.
"Some really great people have picked us up, this guy just ruined everything for us.
"The worst thing is that Anika lost all of her pictures from the last two months that she's been in New Zealand."
Ms Johnsen said she was here over Christmas and received precious gifts from family back home. "Those things just mean the world to me, and he can't use it for anything."
They described the car as a saloon-type grey or brown car, but did not know the licence plate. The man, a European, was in his early 20s.
- BAY OF PLENTY TIMES