Officers have released CCTV images in connection with the first incident, at a property on Ashcroft Close around 5.25pm.
The men tried to get in via a side door and patio door but fled when the occupants heard them and shouted out.
They ran off and got into a waiting white, three-door Audi car before driving off.
A few minutes later, four males forced entry into a property on nearby Deighton Lane.
The only person inside, a woman in her 20s, was locked in the cellar before they made off with jewellery and a watch, leaving in what police believe was the same white Audi.
Three of them are described as Asian males and one as a white male.
Detective Constable Rupinder Ghatrora, of Kirklees CID, said: “Both of these incidents caused considerable distress to those involved and to the wider community, and CID has been carrying out enquiries since 1 January to try and trace those responsible.
“We have released the CCTV images in case it triggers the memory of a member of the public who recognises the clothing or those pictured.
“I would appeal for those living in the area to cast their minds back to 1 January and get in touch with any information you may have.
“I would also appeal for anyone who has seen a car matching the above description to also get in touch with police.”
Call Kirklees CID on 101.