They entered the room by force and took away the jewelry.
A further incident occurred between 11.30am and 2.50pm on Thursday 10 September at a house in the Newburgh Road area.
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Entry to the property was again forced and jewelry and money were stolen.
Officers believe the incident involved a black Ford Ecosport SUV (pictured below).
Detective Constable Lewis McIver said: “We are treating these incidents as being linked and believe the same people were involved in these break-ins.
“Both incidents occurred while the homeowners were not home and the suspects broke into the homes.
“We would like to hear from anyone who saw this vehicle, a dark colored Ford SUV, in the Don Bridge or Royal Gate area in late August or early September.
“We are asking anyone with private CCTV, doorbells or dashcams to view any footage and provide us with anything relevant as soon as possible.
“I would also ask local residents to remain vigilant and report anything of concern to the police as soon as possible.”
Anyone with information is asked to contact Police Scotland on 101 quoting incident number 1944 of September 10. Information can be passed to Crimestoppers anonymously by calling 0800 555 111.