An Audi A6 and BMW 528 had their badges prised off while they were parked in Bellevue Road overnight from Saturday into Sunday.
Subsequent police inquiries established that a further five vehicles have had their badges stolen in the Bellevue Road and McDonald Place area since the weekend.
A police spokesman said: “Not all of the owners have reported these incidents to the police, and we would urge them to contact us if they find that their vehicle has been vandalised.
“We are appealing to anyone who witnessed any of these vandalisms to contact police, and we would also urge anyone else with information that can help us trace whoever is responsible for these vandalisms to get in touch.”
Anyone with any information should contact Lothian and Borders Police on 0131 311 3131, or Crimestoppers in confidence and complete anonymity on 0800 555 111.