Highbury Corner Youth Court was told that Laura Ghodsiam, 59, was sitting on a bench checking her emails at around 9.30pm on November 5 when the pair grabbed the phone from her hand and ran off.
Detective Constable Adele Cashman, 30, was with a colleague when she spotted one of the suspects and gave chase.
But superfit DC Cashman, who competed in triathlons, collapsed on the pavement and died in hospital shortly afterwards. Doctors have not yet discovered the cause of her death.
Valerie Benjamin, prosecuting, said: "The woman was walking home along Haverstock Hill when she decided to have a rest and sit down on the bench near a bus stop.
"While sitting there she began checking her emails on her phone when she noticed a hand reach over her and take it.
"She saw the two defendants run away. They were chased by the woman, who was shouting, 'Get them, get them'.
"Two police officers were walking nearby and noticed the victim shouting , they ran to join in the chase."
As the officers chased the two muggers they radioed for support.
Responding to the call DC Cashman and her colleague, who were in a police car nearby, sped to the scene in Belsize Gardens and chased after one of the muggers.
But just minutes later DC Cashman collapsed to the ground. She was rushed by ambulance to the Royal Free Hospital but died around an hour later.
The iPhone was recovered intact when another officer on the scene and the victim activated its internal tracker which showed it had been thrown into a hedge near Belsize Road.
The two 17-year-olds were arrested at the scene and were charged with theft.
Dressed casually in blue jeans and a beige jumper, and jeans and a blue zip-up sports jacket, the two teenagers stood with their hands in their pockets as they both pleaded guilty to the mugging today.
Sentencing them both to a six-month referral order, Paul Brenells, chairman of the bench, said: "You are both going to end up in serious trouble if you continue on this path.
"You are both educated and have good prospects, but if you continue on this path you are going to wreck your lives.
"You are not going into custody but if you carry on with this sort of thing you will very quickly end up in custody."
The court heard that the pair are in sixth form college and both hope to go on to university.
One of the muggers apologised to the court for the theft, which he blamed on getting "caught up in the atmosphere".
He said: "I would like to say I am sorry for committing a crime. Usually I am not the kind of person who would commit a crime, I just got caught up in the atmosphere."
The pair were also each ordered to pay costs of £42.50.
