Police Scotland said the two incidents had taken place in the Abbeyview and Touch areas over the past week.
PC Fraser Laird issued a warning over bogus callers.
“Incidents such as this are extremely rare, but demonstrate the methods criminals will use to get into houses,” said the community safety officer.
“Bogus callers operate all year round and will target the elderly and vulnerable, and you should never allow anyone to enter your house unless you are aware that they are coming.
