Scottish SPCA officers recovered the sparrowhawk from Portobello High School in Edinburgh at about 7.45am on Monday.
A few minutes later the charity rescued a long-eared owl which was found lying in a field in West Linton in the Borders.
Animal rescue officer Stephanie Grant took the injured birds to the Scottish SPCA's wildlife rescue centre at Fishcross near Alloa, Clackmannanshire, where they are recovering.
She said: "The sparrowhawk had managed to get itself trapped behind the netting, which is designed to deter pigeons from landing on the roof of the building.
"It had a sore beak, possibly from bashing off the walls while trying to escape, and it also had quite a large lump on its wing.
"Our vet believes this is an old injury the hawk might have received from another bird, which has then become infected.
"The long-eared owl was found grounded beside a fence and he has a shoulder injury which should heal with a few weeks' cage rest.
"We are hopeful both birds will make a full recovery after some recuperation and rehabilitation.
"We'd love to return these stunning creatures back to the wild, where they belong."
Anyone who discovers an injured or distressed animal should call the Scottish SPCA animal helpline on 03000 999 999.