The 93-year-old and 88-year-old victims, who are both housebound and rely on help from carers and friends, were targeted at their home in the west of Edinburgh some time between July and August. Police believe those responsible may have had some knowledge of the sisters' care provision.
Alan Gall, chairman of Crimestoppers Scotland, said: "This is a particularly despicable crime. The culprit has chosen to prey on the vulnerabilities of two elderly members of our community.
"One of the sisters has not even been made aware of the theft as it is believed she would react very badly to the news and that this may be detrimental to her health."
Detective Sergeant Neil Spowart, of Police Scotland, said: "Clearly those responsible have targeted these women, as they know they can offer no resistance."