The antiques, valued at between Â£2,000 and Â£3,000, were taken from Osterley Park House in Twickenham, south-west London, on 16 July.
They were taken from a locked cabinet in a room that was closed to the public due to a wedding at the house.
The pieces have images of Russian ruler Catherine the Great and Prussian king Frederick William II, and were made between 1770 and 1775.
The cups and saucers, which are made of Berlin porcelain, are described as dark blue and painted 'en grisaille' with heavy gilding, flower sprays, finials and branch handles.
Det Con Ray Swan, from the Mets Art's and Antiques Unit, said: "The cups and saucers are of significant historical value, we believe that whoever took them specifically targeted these pieces.
"We would urge anyone who may know of their whereabouts to come forward as they may hold vital information to help us catch whoever was responsible for this burglary."
Two 300-year-old cups with saucers have been stolen from a country house.