Westenra's parents, Jill and Gerald Westenra, have two other children, Sophie and Isaac. The family has a history of music: Westenra's grandmother Shirley Ireland was a singer, and her grandfather was a pianist who also played the piano accordion.

Her pursuit of a musical career began at the age of six, when she was cast in the lead singing role of "Little Star" in the Christmas play at her school, Cobham Intermediate. After the show, a teacher who had watched the performance approached her parents to tell them that their daughter was pitch perfect. The teacher encouraged Westenra to learn how to play a musical instrument to improve her abilities, and she duly learned to read music and play the violin, piano, and recorder. She began voice lessons and discovered a passion for musical theatre. By age 11, she had performed more than 40 times on stage but was often given male parts: "I got boy parts quite often. In ballet, there were not enough boys. So they ended up choosing half