It’s been 18 years since the Vigiano brothers — Joseph, an NYPD detective, and John, an FDNY smoke-eater — ran headlong into the hell of ground zero and lost their lives as they helped save others.

But their family still honors the siblings’ sacrifice — and they aren’t alone.

Joseph’s three sons, his widow and the fallen brothers’ mom met Wednesday with President Trump in Washington, trading handshakes, mementos and loving remembrances of heroes lost but never forgotten.

“I’m very proud,” Kathy Vigiano, herself a retired cop who met her husband on the job and now lives on Long Island, told The Post. “It’s very special that he’s [Trump] remembering Joe 18 years later.”

“He’d get a kick out of it and have a big smile on his face,” she said of her husband.

The White House brokered the emotional meeting with middle son James, a Marine corporal who appeared in a USMC video last year about the significance of his service on the USS New York, which is made from 24 tons of steel harvested from the wreckage of the World Trade Center.

Before meeting the family outside the Pentagon, Trump gave them a shout-out in a speech at the site, itself struck on 9/11.

“You have sacrificed beyond measure,” said Trump, addressing the family. “And you will never, ever stop giving back to this country. … Thank you.”

At the time of the brothers’ deaths, Joseph’s three sons were just 8, 6 and 3 months old.

But they met Trump on Wednesday as adults — and heroes in their own right.

Jarhead James traded salutes with the president, while NYPD cop and Marines reservist Joe Jr. and youngest John, a freshman at SUNY Maritime College who plans on applying to both the NYPD and FDNY, opted for handshakes.

James’ fiancée, Jessica Wiggins, and John and Joe Sr.’s mother Jeanette Vigiano was also in attendance, the family said.

Joe Jr. gifted the president with a challenge coin — a commemorative token popular in police and military circles — from Brooklyn’s 75th Precinct, where his parents met and he now serves.

Trump reciprocated by presenting each of the sons with a presidential challenge coin, before the family was led on a tour of the White House.

“Everything went really well. The president was a gentleman,” Joe Jr. told The Post. “It was very special that he could keep the memory of my father and my uncle alive 18 years later.

“I’m sure my father’s smiling down.”

Additional reporting by Aaron Feis