Her husband, Michael Bacher, said he met "the most wonderful mother and wife you could have ever wished for" at a gliding club in Matamata many years ago.
He was struck by the "outstanding, lovely person" who was "very skilled and very professional and a lot of fun".
But most of all, he was taken by her "smile that lit up the whole room".
"She really was one of the most outstanding females in the aviation industry. She touched many, many lives. She was the perfect mother and the perfect professional at the same time. It's just too early and devastating and completely unexpected."
Daughter Bianca Barbarich-Bacher said her mother was the best "you could ever, ever imagine ... She was an incredible pilot and role model and a really incredible lady. She was always so bubbly and had such an incredible personality."
Her mother also inspired her to take up recreational flying.
Air New Zealand said Captain Barbarich had been in the process of switching from the Boeing 747 to the Dreamliner, the airline's newest plane. She had just landed the jet, with four pilots on board as part of a training programme, when the medical emergency occurred.
A passenger told the West Australian newspaper they hardly noticed anything had happened.
"The approach to Perth and landing was smooth and there was only a slightly heavier braking on the runway than was noticeable."
Air New Zealand chief pilot David Morgan said Captain Barbarich was at the controls and the aircraft landed normally. "Unfortunately after landing she became seriously ill."
In an internal statement sent to staff, Captain Morgan said: "Ann's friendships with other Air New Zealanders extend well beyond flight operations and safety and she will be sorely missed by many people right across the business."
New Zealand Association of Women in Aviation president Sue Telford said Captain Barbarich would leave a huge gap in the association's pool of knowledge as one of its most experienced commercial pilots.
"Ann basically blazed the trail. She did her helicopter flying, she was a parachutist, she did gliding - so she also had quite an extensive general aviation background."
Ms Telford described Captain Barbarich as a very gracious woman who was known to take fledgling pilots under her wing.
"She's going to have a big send-off," Ms Telford said.
Captain Barbarich's family were expected to accompany her body back from Perth early today, to be met by an Air New Zealand guard of honour in full uniform at Auckland Airport.
Her funeral will be at the Holy Trinity Cathedral in Parnell next Friday.
In lieu of flowers, the family have appealed for donations to be made to Koru Care.
