Nine were damaged at Salamander Court between midnight and 7am. Most had their wing mirrors knocked off.
A further three cars were damaged in a similar way in Tolbooth Wynd around 4am.
A woman who was seen in the area of the second incident is being sought by police and investigations are underway to see if the incidents are linked.
The woman is described as being white, 18-20-years-old with long straight dyed black hair, and was wearing a red waist-length coat.
Sergeant Colin Johnston said: “We are keen to hear from anyone who may have been in Salamander Court, and who may have seen someone acting suspiciously, in the early hours of yesterday morning. “A number of people are now facing repair bills as a result of this mindless vandalism, and we are doing all we can to identify whoever is responsible for it.”
Anyone with any information should contact Lothian and Borders Police on 0131 311 3131, or the independent charity Crimestoppers anonymously on 0800 555 111.