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.

Reporters said they appeared healthy but a little distressed after their long journey.
A circus surrendered some of the lions, while others were taken in raids.
The US-based group Animal Defenders International (ADI), which was behind the action, says almost all the lions have had teeth or claws removed.
They would not survive in the wild.
The lions are being transferred by land to the Emoya Big Cat Sanctuary, a 5,000-hectare reserve in northern South Africa. There, the lions will have drinking pools, platforms, toys and veterinary care.
"This is a hugely important rescue mission because it does make a statement around the world about the way people treat animals," ADI spokeswoman Jan Creamer said.
"These lions have suffered tremendously."
The first group of nine lions was collected in Colombia's capital Bogota on a cargo plane, which then flew to Peru's capital Lima to pick up 24 more animals.
"It will be hugely satisfying to see these lions walking into the African Bush," ADI Vice-President Tom Phillips was quoted as saying by the Associated Press news agency.
The lions were freed after the use of wild animals was banned in Peru in 2011 and Colombia in 2013.
The 5,000-hectare (12,355 acres)  Emoya Big Cat Sanctuary is on private land and already houses six other rescued lions and two tigers.
The lion habitats there would be steadily expanded over the coming months as the lions became familiar with their new life and were introduced to each other, said ADI.
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.
[NEXT_CONCEPT]
More than 30 lions rescued from circuses in Colombia and Peru have been flown to South Africa to start a new life in a sanctuary.