PC Emma Rae and PC Karen Gunnill have been nominated for the National Police Bravery Awards to be held in October.
In January last year, PC Rae was patrolling Ecclesall Road in a public order van when a call came in from CCTV operators alerting officers to a firearms incident.
Cameras had captured a man firing at least one shot from a gun near to the Kettle Black bar and then pistol-whipping a man who was later found to have a fractured shoulder resulting from the incident.
The gunman then fled the scene in a taxi.
Despite being unarmed, PC Rae followed the cab in her van and radioed in a description of the vehicle and suspect.
She kept tracking the taxi while firearms officers were called to intercept.
Before the armed officers arrived, the gunman stopped the taxi and got out, paid the driver, then ran off in the direction of Ponderosa park, Upperthorpe.
Knowing he had to be detained to protect the public, PC Rae ran after him.
PC Karen Gunnill, who had been patrolling the area, spotted Premi during the chase and saw him reaching for his waistband.
Believing he was reaching for his gun, the officer produced her Taser stun gun and challenged him to stop before firing at him when he failed to comply.
He was incapacitated and the PC Gunnill and PC Rae were able to make an arrest.
Premi was found to be carrying a lock-knife, having discarded the gun - an imitation air weapon - before his arrest.
He was jailed for three years over the incident.
South Yorkshire Police Federation Chairman, Steve Kent, said the officers’ actions made them worthy nominees for the award.
“As far as our colleagues knew this man was carrying a firearm and had already inflicted an injury on a member of the public,” he said.
“They are police officers though. And they carried on towards that danger with one thought in their minds. To protect the public from this dangerous individual.
“The officers knew he had to be detained as soon as possible and showed incredible determination and bravery to get the job done. We are very proud of them both.”
The National Police Bravery Awards honour officers from across England and Wales who have performed outstanding acts of bravery while on or off duty.
John Apter, National Chairman of the Police Federation of England and Wales, said: “We are incredibly proud of all the nominees from across England and Wales. The actions of these courageous officers provide a small snapshot of the amazing work our colleagues carry out day in and day out.
“PC Emma Rae and PC Karen Gunnill proved once again how brave our colleagues across the country are. They had no idea that this was not a real weapon. What brilliant and courageous police work. We are very proud of them.
“As a Police Federation, we wanted to make sure these brave officers received the recognition they deserve.”