The police officers who were called to the incident decided to donate £200 to the family from the force's Tuck Shop.
Sergeant Richard Markham, from West Midlands Police, which are investigating the burglary, said:
"Stealing children's Christmas presents is such a heartless and callous thing for anyone to do. We wanted to try and put a smile back on their faces for Christmas.
"We're determined to track down whoever did this and would urge anyone with information that could help to come forward.
"If you know who is responsible please do the decent thing and call us before those responsible cause heartache like this for another family."
More top news
A cold night, with clear spells developing for most. Tomorrow, generally fine and dry with plenty of sunshine, especially in the morning.
Clearer and colder overnight than of late, with many areas remaining dry. Isolated blustery showers may affect the Peak District at times.
Spring is literally around the corner and signs of it are starting to pop up. We would love to lots of pictures from all around the Midlands