The man, 65, then let the pair – dressed in suits and wearing earpieces – into his home in Kennedy Drive, Airdrie.
Once inside one of them held him in his bedroom, while the other stole gold jewellery, a purse and medals.
The pensioner was then left in a common close before the men escaped on foot.
Officers want to speak to anyone with information or who may have seen the men.
Detective Chief Inspector Pat Campbell, of Motherwell Police Office, said: "This was a brazen and despicable attack which has left an elderly man very traumatised. We are doing everything in our power to catch the men responsible."
Descriptions of the assailants have been released in a bid to help trace them.
The first man is described as being about 5ft 4in tall, wearing a dark suit, black jacket and glasses.
The second man was about 6ft and was also wearing a dark suit and black jacket.
As a result of the attack, Mr Campbell has warned residents against letting people into their homes without identification.
He added: "I'd like to remind everyone, particularly elderly members of the community: if anyone comes at your door, always, without exception, ask them for identification.
"A police officer should show you his or her warrant card.
"Ask them which station they've been deployed from, then close and lock your door while you contact the station to check they are genuine.
"Use your door chain to ensure they cannot gain entry until you are satisfied with their identity."
Anyone with any information about the crime is asked to contact the CID at Motherwell Police Office on 01698 483000 or Crimestoppers anonymously on 0800 555111.