Claremont is an incorporated town in Surry County, Virginia, United States. The population was 378 at the 2010 census. A granite marker is a memorial to British settlers' arrival in the area. It received its name during the colonial era from the royal residence in Surry Shire in England. The town was incorporated in 1886, had a port on the James River, and gained railroad service as a terminus for a while before being abandoned.