"calling after" is correct and can be used in written English.
For example: She ran out the door, calling after him to wait.
Please state your reason for calling, after the beep.
Then Real Madrid came calling after sacking Carlo Ancelotti.
Corporate sponsorship is up, and American television has come calling after two decades of indifference.
To get the full amount they must keep calling after the baby is born.
That did not stop him from calling after he returned to Berkeley.
"There were people crying out for help, calling after members of their family.
He said he found his life's calling after stumbling upon Dr. Rao's class.
The teenage girl came running out of Behm's Family Restaurant, calling after me.
Like the insurgent's friend calling after him: just a misplaced word.
But forget about how it'll sound in the classroom; that's not where you'll be calling after it.
He realized basketball was his life's calling after seeing a teenage Connie Hawkins playing summer league ball in 1959.
