Ashley Dodd, 28, rang his victims claiming to work at the George Eliot Hospital in Nuneaton.
Dodd, of Hayes Lane, Exhall, Warwickshire, claimed he had been "messing around" while drinking.
He was handed a 16-week prison sentence at Nuneaton Magistrates' Court after he previously admitted eight offences under the Malicious Communications Act.
Magistrates previously heard Dodd chose his victims at random after he had been binge-drinking on 6 and 7 June.
His actions caused families "shock and devastation", the court was told, with some taking several hours to trace their children to find they were unharmed.
Det Con Michelle Russell, of Warwickshire Police, said the calls were "extremely upsetting" for the victims.
"We are pleased that Mr Dodd has been brought to justice and hope it will bring some comfort to the families," she said.
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