Stacey Burrows, 16, and Lucy Pygott, 17, were killed while on a training run in Aldershot, Hampshire, on 8 November.
Judge Phillip Gillibrand revealed he had lost his own brother in a car crash as he expressed sympathy for the girls' relatives.
Michael Casey, 24, is charged with causing death by dangerous driving.
Mr Casey, of St Paul's Road, Tottenham, London, was bailed to appear at Winchester Crown Court on 13 April.
Addressing the teenagers' relatives, Judge Gillibrand said: "I do not know the incident but I myself lost my brother in a road traffic accident.
"I know the trauma and the anguish you must be going through."
He was interrupted by a member of the public knocking on the window of the public gallery.
The judge asked them to leave the court and for people to "respect the rule of law" in a case where "emotions are flying high".
During the short hearing, Mr Casey spoke only to confirm his name, address and date of birth.
He did not enter pleas but the court was told he was likely to do so when the case is next heard.
The girls, who were members of Aldershot, Farnham and District Athletic Club, were warming up for an evening run when they were hit by a black Ford Focus in Queen's Avenue.
Lucy Pygott, who was from Hartley Wintney, Hampshire, had won a 3,000m bronze medal at the European Youth Championships in July.
Stacey Burrows, from Farnborough, was the Hampshire under-17 3,000m champion.
A judge has told a court he understood the "trauma and anguish" of the families of two teenage athletes who died after being hit by a car.