Neil and Jackie Stewart, who had been holidaying in Peru, arrived in Lima on March 16 and were due to fly to Colombia the next day but the Colombian border was suddenly closed.
In a recent email sent to the newspaper, the Stewarts said they had "maxed-out" their credit card to ensure they had confirmed bookings on the special flight.
They had received a phone call from the New Zealand embassy in Santiago in Chile and were told if they were having trouble paying the fare, they could apply for financial aid.
"What was available to use was unclear, so we maxed out our credit card to pay the almost $11,000 to get home.
"But we realise some people won't be in a position to do that," they said.
Last night Prime Minister Jacinda Ardern announced final preparations were under way for an evacuation flight to get New Zealanders stranded in Peru back home.
She said close to 70 people had registered for the flight, including a small number of Australians.
The Ministry of Foreign Affairs and Trade confirmed today 41 New Zealand citizens, permanent residents and persons ordinarily resident in New Zealand boarded the charter flight in Lima.
Another 18 people had registered to board the same flight from Santiago in Chile.
The ministry said the flight left Lima at 6am today for Cusco in Peru and flew onto Santiago just before 8am.
The ministry spokesperson said the flight would stopover in Santiago as per the agreement with the Chilean government to allow necessary transit through Chile.
The flight was scheduled to depart Santiago at 4.30pm today and then fly directly onto Auckland arriving at 5am tomorrow. Neil Stewart's sister Lynne, who lives in Greerton said she had an email from her brother and sister-in-law on Sunday, and at that point, they were still waiting for confirmation the flight would go ahead.
"I'm so relieved things are starting to look more positive. I will be crossing my fingers, my toes and anything else I can cross until they finally land in Auckland," she said.
"It's been a very anxious and emotional time, not only for Neil and Jackie. We can't wait until they are back home safe again, but they've got a long journey ahead of them.
"We know when Neil and Jackie finally land in Auckland they'll be absolutely exhausted, but I'm sure they will be overjoyed too, despite having to stay in isolation for another two weeks."
Lynne said just being to phone her brother and sister-in-law and hear their voices rather than have to rely on emails back and forward would be a "huge blessing" too, she said.
