Ekenæs was born in Oymark, the current Marker municipality, but her father died when she was young. She, and her mother, Mathilde Amundsen (1870-?) moved to mother’s sister on the farm Hønstvet in Skiptvet. Elisabet and her sister Karoline (1903-?) got very good grades in school, especially in mathematics and Norwegian language. She was born with a club foot. She moved to Oslo. Ekenæs stayed for a long time in Valerenga neighbourhood. Her niece, Jorunn Elisabeth Kleppe, lived with her for over 10 years. Also, Ekenæs’ mother lived with her in 1950s. She worked as a school teacher for a Mollergata’s church. She was devout, never smoked, and never drank alcohol.
On 26 December 2016, Ekenæs celebrated her 112th birthday, becoming only the second person in Norway to attain this age (Maren Bolette Torp was the first person in Norway to reach the age of 112).
Ekenæs died on 4 January 2017, aged 112 years, 9 days. She was the first validated supercentenarian death of 2017. She had been Norway’s oldest person for more than four years.