She made a number of important ascents in the Alps in the 1860s and 1870s, but was thwarted in her two greatest alpine ambitions: to be the first woman to climb the Matterhorn, and the first person to climb the Meije in the Dauphiné. In contrast to Walker, who always wore dresses, Brevoort was the first female mountaineer to wear trousers. Meta Brevoort was the aunt of West. A. B. Coolidge, whom she brought to Europe in 1865, when he was 15 years of age, and introduced to alpine climbing.
Coolidge eventually became an outstanding mountaineer, with over 1,700 ascents in the Alps, and the greatest alpine historian of the Victorian age.
She and Coolidge journeyed to the Dauphiné several times in order to attempt the Meije, but encountered bad weather each trip.