A university hall of residence, Sorby Hall, built in the 1960s and demolished in August 2006, was named after him. He died in Sheffield and was buried in Ecclesall churchyard. He was elected a Fellow of the Royal Society in June 1857 as one who was "Author of various papers on Slaty Cleavage; on the peculiarities of stratification due to the action of currents & their application to the investigation of the Physical Geography of ancient periods; on the microscopical structure of limestones and other peculiarities of the physical & chemical constitution of rocks. Distinguished for his acquaintance with the science of Geology.". He delivered their Bakerian Lecture in 1863 for his work "on the Direct Correlation of mechanical and Chemical Forces" and was awarded their Royal Medal in 1874. In 1892, Sorby was elected a Foreign Honorary Member of the American Academy of Arts and Sciences. Both the International Association of Sedimentologists and the Yorkshire Geological Society have Sorby Medals named in honour of his achievements in geology. The Henry Clifton Sorby Award is offered by the International Metallographic Society in recognition of lifetime achievement in metallurgy. The University of Sheffield has a chair of geology/physical geology named after him and the Sorby Natural History Society is named after him. The area in which the society operates (north East Derbyshire, the Sheffield and Chesterfield areas) are known to members as 'Sorbyshire'. Dorsa Sorby on the Moon is named after him. There is also a wing at the Northern General Hospital named after him.