They were stolen by a man who went into the Robert Anthony store on Rose Street to enquire about engagement rings.
He snatched the rings, which have a combined value of £21,000, after a second man came into the shop and distracted the other member of staff working there.
The pair then made off west along Rose Street.
Police Scotland appealed for information about the incident, which happened at about midday on Saturday January 4.
Detective Constable Gavin Watson said: “The suspects did not threaten the staff members in any way but used distraction tactics and seized on the opportunity to make off with two valuable engagement rings.
“We are keen to hear from any members of the public who were on Rose Street on Saturday afternoon and remember seeing anyone or anything suspicious in the area.
“In addition, anyone who recognises the description of these men and can help identify them is also asked to contact police immediately.”
The first man is described as white, late twenties to early thirties, wearing a khaki fleece and trousers and a khaki winter hat with earflaps.
The second man is described as white, mid to late twenties, wearing a heavy winter jacket and a winter hat with earflaps.
On its website, Robert Anthony Jewellers describes itself as one of Scotland’s leading pearl and diamond specialists.