Six Welsh farming organisations united to create the award for the retired sheep and beef farmers.
The function was held at Chatsford Village in Mosgiel on January 9.
Mrs Neilson, who has dementia, lives in the retirement village.
"This is a deeply moving and emotional moment in our lives," Mr Neilson said, trying hard not to cry.
The couple visited Wales in the 1970s, when Mr Neilson was a Nuffield scholar.
On the trip, a Welsh farmer asked if his nephew could visit them in New Zealand.
An invitation was extended and in 1978, the young Welsh student was the first of more than 100 of his counterparts to live and work on their sheep and beef farms for about four months from spring.
He praised his wife for creating a warm, friendly and delightful "home away from home" for the visitors.
"A mighty big thanks to you, Ailsa."
The function began with the more than 40 people attending standing for the Welsh and New Zealand national anthems.
Sheep and beef farmer and Welsh expat Graham Evans, of Owaka, presented the couple with the award, which was made of slate.
"Every house I grew up in had a slate roof. It is ingrained into our culture. I hold slate very dearly."
Presenting the award to the couple was a privilege, he said.
It was a major achievement to get the Welsh farming organisations to unite, Mr Evans said.
He recalled Mrs Neilson serving Welsh students roast lamb for dinner and pavlova for dessert.
"That was a highlight for most of them."
Several video messages from Welsh people were played at the ceremony and related the "second-to-none" hospitality and the farm being a "school of excellence" where "a glass was always half full".
