It happened at about 8.10pm on Sunday, May 26 when the two children fell 10 feet down onto a ledge in Baildon Bank, Bradford.
The girl and boy were rescued by the police, fire and ambulance crews.
They were not injured.
Paedophile arrested at Leeds Bradford Airport after travelling from Ireland to meet ‘13-year-old girl’
Developers admit planning breaches in construction of Leeds retirement flats
Met Office issues thunderstorms and torrential rain weather warning for Leeds as heatwave comes to abrupt end
Aasia Majeed: Police launch urgent appeal to trace Leeds mum missing with one-year-old child
Andre Rieu, Europe's Strongest Man and Magic Mike Leeds Arena shows could be at risk if city wins Eurovision bid
West Yorkshire Sergeant T Green, who is a neighbourhood policing team sergeant for Baildon, Shipley and Wharfedale, shared the incident on Twitter.
He said: "Children stuck on Baildon Bank rescued by Police, Fire and Ambulance all working together."
West Yorkshire Fire and Rescue Service confirmed that the children were trapped 21ft up after falling 10ft down onto the ledge.
A two line rescue system was set up to lower them to the ground.
The technical rescue unit from Cleckheaton and a specialist technical rescue officer attended.
Fire engines from Shipley, Bingley and the aerial from Bradford were also there.