Two men broke into a home on Main Street, East Calder, between 7pm and 8pm on Saturday, February 13, one armed with a spade.
They demanded the girls, aged 8 and 12, hand over what police described as a “quantity of cash”, before fleeing the scene.
Officers confirmed that the children were left shaken by the incident but unharmed.
Detectives are now appealing for information from the public to help identify the two men responsible.
They called for witnesses to come forward, as well as those who may have CCTV.
Police said the first suspect was wearing a black jacket, black joggers and a balaclava style mask, which covered his whole head.
The second suspect is thought to have been wearing a beanie hat and was carrying a spade.
Detective Constable Ross Collett, from Livingston CID, said: “We are carrying out extensive enquiries, including examining CCTV and will be asking for the assistance of local householders, as we work towards identifying the suspects involved and bringing them to justice.
“If you have any information, or saw anything suspicious in the area around the time of the break-in, we are encouraging you to come forward and assist our investigation, especially if your household has CCTV.”
Anyone with information can contact police on 101, quoting incident 3611 of 13 February. Alternatively, you can call Crimestoppers on 0800 555 111, if you wish to remain anonymous.