Mrs Eckford, an itinerant music teacher, has owned the hand-crafted viola since 1995.
It was made by Malcolm Collins, an acknowledged master of the art of instrument making. He hand-crafted it for Mrs Eckford and it is designed for people with small hands.
"It's a work of art," she said.
Mrs Eckford had taken the viola to school on Friday, and "didn't think about taking it home".
Although she would not put a price on it, she bought it for thousands and thought it would be worth more now.
Mrs Eckford, who trained as a pianist, decided to learn viola as an adult.
"It's beautiful, even if you don't make a nice sound," she said.
"A stringed instrument is somehow slightly more emotional."
Mrs Eckford said she won't replace the viola.
"If I get it back I'll be over the moon.
"I would like it back please."
The missing saxophones will also impact on the students, as six people have signed up for lessons.
"I'm going to have to say to someone on Monday 'I'm sorry'," she said.
Mrs Eckford teaches at Masterton Intermediate School, Wairarapa College, Rathkeale College, and St Matthew's Collegiate School.
She also conducts Wairarapa Community Orchestra and Wairarapa Youth Concert Band.
Police are continuing with their inquiries, and anybody with information should contact them.