The theft took place on May 28 when the Grade II* building was broken into and the silver was taken from a locked display case.
Dr Joan Unwin, archivist at the hall, has issued a list of the missing items in the hope the trade can identify any of them.
Among the missing collection is a 2ft 4in (70cm) silver presentation salver; a 1783, 6in (16cm) high George III candlestick; a 1773 George III coaster with pierced sides by Marsden, William & Co or Richard Morton & Co; and a Walker & Co silver plate Christening mug with decorated border.
For the full list and images contact Colonel Philip Bates, CEO of the Company of Cutlers in Hallamshire, on Philip.email@example.com
Anyone with information on this incident should call 101 quoting crime reference number 14/825513/21 from Sheffield Police or call Crimestoppers anonymously on 0800 555 111.