In 1871, the Cranch Public School Building, named in Cranch's honor, opened at the southwest corner of 12th and G, SE in Washington, D.C. It was demolished in 1949.^[38]

Cranch was elected an Associated Fellow of the in 1809.^[39]

Cranch was elected as a member of the in 1813.^[40]

During the 1820s, Cranch was a member of the prestigious society, , who counted among their members presidents Andrew Jackson and John Quincy Adams, and many prominent men of the day, including military officers and officials of government service, and leaders of medical and other professions.^[41]