This ring was taken from a home in Warren Lane, Friston, at some point after the middle of October, along with several hundred pounds in cash and a second ring.
The ring in the photograph, which is gold and fitted with a pear-shaped diamond, is worth around £4,000.
The second ring that was stolen was a gold wedding ring, also set with a diamond and worth more than £3,000.
Sussex Police launched Operation Magpie to tackle burglary across the county.
PC Charlotte Cox said: “The victims contacted us after they noticed that a number of items around their home had gone missing although there had been no sign that they had been broken into.
“I would like to speak to anyone who may have seen anyone acting suspiciously in Warren Lane over the last few months and who could describe them to us.
“I would particularly like to speak to anyone who may have been offered the chance to buy the rings.
“If you have seen them or know where they could be, please contact us.”
Anyone with information should email firstname.lastname@example.org quoting serial 1319 of 23/11, call 101 or contact the independent charity Crimestopppers anonymously on 0800 555111.