The latest pockets of disorder arose out of ongoing tensions and widespread protests over the restriction of the flying of the Union flag at Belfast City Hall.
All nine youths were arrested for public order offences in Lisburn, where police said serious disorder had flared.
Five of the children - including the 11-year-old - were arrested in the Hillsborough Road area.
In the Longstone Street area, a 14-year-old, two 15-year-olds and one 17-year-old were arrested - as was a 31-year-old man.
Many of the injured police officers were among those who came under attack from a group of up to 200 loyalist protestors in east Belfast, as they dealt with disorder on the Lower Newtownards Road.
There were also reports that a journalist had been attacked in that area.
While most of the protests were peaceful, the violence witnessed in some areas tonight is totally unacceptable.
PSNI ACC Dave Jones
One officer was injured during trouble at Sandy Row in the south of the city, where missiles were thrown and a car was also set on fire.
A 25-year-old man was arrested in nearby Bruce Street area and an 18-year-old was arrested in the Blythe Street area of the city.
UTV also understands that a police officer was hurt in Portadown after a bottle was thrown in the Shamrock Park area of the town.
In a separate incident in the town, a man was taken to hospital after he was knocked down by a car on the Northway during a flag protest.
Local MLA and SDLP deputy leader Dolores Kelly said she feared that more serious injuries could be sustained if the violence wasn't brought to an end.
"This is a time of year when people should be looking forward to a welcome break and sharing some valuable time with family and friends," she said.
"These protests are causing people to live in fear and that is totally unacceptable."
A 19-year-old man was arrested after a firework was thrown at police in Armagh, during a protest attended by about 150 people.
In Carrickfergus, police are investigating after a number of protesters stormed the town hall where a public meeting was disrupted and a number of public representatives were threatened.
A 30-year-old man was arrested in the Minorca Place area for public order offences.
In Ballymena, police say a 20-year-old man was arrested in the Crebilly Road area - also for public order offences.
In Omagh, Sinn Féin West Tyrone MLA Declan McAleer hit out over a protest which he said saw "masked youths lay siege to the town centre".
He added: "As a community activist who helps to organise charity walks and other local events, I was intrigued how the organisers managed to get the protest approved without giving 28 days notice.
"People are getting fed up with our town being disrupted and held to ransom by a handful of protestors."
Those who engage in illegal protests are destroying their own community and doing serious damage to the local economy and, frankly, they are ruining Christmas for the whole of Northern Ireland.
Conall McDevitt, SDLP
Around 80 protests took place across Northern Ireland as the row over the restriction of the flying of the Union flag at Belfast City Hall entered its third week. A total of 15 people were arrested.
PSNI Assistant Chief Constable Dave Jones has described the situation in Northern Ireland as "corrosive" and is calling for dialogue rather than protests.
"There were arrests and more will follow as we now trawl through evidence gathered by officers out on the ground," he said.
Since the start of the protests, 41 police officers have been injured while dealing with violence.
A total of 59 people have been arrested so far - 42 of them have been charged, four have been reported to the Public Prosecution Service and 13 have been released on police bail.