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 woman celebrated her 100th birthday by returning to Wicksteed Park in Kettering where she grew up.
A man has died after his car plunged into a canal in Wednesbury last night.
An investigation is underway after the bodies of a man and a woman were found in a house in Digbeth.