Armsby received widespread recognition during his lifetime. He received honorary doctorates from the University of Wisconsin (1904), Yale University (1920), and Worcester Polytechnic Institute (1921). He was elected a member of the National Academy of Sciences, the Royal Society of Arts, and the Royal Swedish Academy of Agriculture and Forestry. He was awarded a gold medal at the Panama-Pacific International Exposition in 1915 for his model of the calorimeter he had designed at Penn State. A U.S. Department of Agriculture report called him "the foremost exponent of research in the field of animal nutrition in the country and an international authority."