It has become as much a part of modern-day sports celebrations as cutting down nets, stripping off sweaty jerseys, dousing coaches with Gatorade and braying, “I’m going to Disneyland!” From the Little League World Series to the NFL’s Super Bowl, no American sporting title is complete without a visit to the White House and personal tribute from the Commander-in-Chief.

In the past 12 months, President Obama has hosted the champions of every major professional league, as well as the 2012 U.S. Olympians, NASCAR driver Brad Keselowski and a slew of NCAA squads. His predecessor, George W. Bush, stayed equally busy feting sports stars, including Uno, the beagle that won the Westminster Kennel Club’s Best in Show in 2008.

Tuesday brought another twist to the White House tradition that shows no sign of abating, with Obama dipping four decades back to honor the 1972 Miami Dolphins, who defeated the Washington Redskins in the Super Bowl to complete the only unbeaten season in NFL history.

The 31 former Dolphins who trouped into the East Room of the White House, along with their Hall of Fame Coach Don Shula, bore the years well for the most part. Wide receiver Paul Warfield was as trim as Obama himself. Larry Csonka’s mustache was bushy as ever. And Shula still sported a shock of white hair and that chiseled jaw. Collectively they have signed untold autographs and cycled through nearly as many marriages, divorces, second careers and joint-replacement surgeries in the last four decades.

But on Tuesday, they were reduced to wide-eyed children on the field trip of a lifetime, gamely taking their place on risers behind the president with youngsters’ vigor and a pride that made each stand a little taller.

Most acknowledged the honor wouldn’t have resonated as deeply in their youth, when they sat atop the sporting world, setting records on the field and raising hell off it.

Former tight end Marv Fleming, a veteran of five Super Bowls and the driving force behind the belated honor, equated the visit to “another Super Bowl of a different kind.”

Ex-quarterback Bob Griese’s only lament was that his mother, Ida Marie, hadn’t lived to hear tell. “She’s up in heaven high-fiving everybody and telling them her son is going to the White House,” Griese said on the eve of the ceremony.

None was more humbled than kicker Garo Yepremian, born in Cyprus to Armenian parents.

“I came to America when I was 22 years old with hopes of getting a scholarship and going to school,” said Yepremian, 69. “And here I am, 47 years later, going to the greatest house in the world — the White House — in the free-est country in the world, the greatest country in the world, the most giving country in the world, the most forgiving country in the world.”

Presidential honor

The tradition of U.S. presidents hosting sports champions dates to Andrew Johnson, believed the first to invite a baseball team to the White House, according to William B. Bushong of the White House Historical Association.

Though Richard M. Nixon was an avid NFL fan, frequently phoning Shula with suggestions for offensive plays (as well as the Redskins), including a slant route that already was part of Griese’s repertoire, he hadn’t invited the Dolphins to the White House following their Super Bowl triumph. The practice became routine under Ronald Reagan, who formalized the proceedings, with the president welcoming each championship team, then yielding to the coach or star player who typically presented the Commander-in-Chief with a commemorative jersey.

Obama relished the role Tuesday, hailing Shula and his players as “men of accomplishment and character” and enumerating their many superlatives en route to their 17-0 record, capped with a 14-7 Super Bowl victory over George Allen’s Redskins.

With backup Earl Morrall taking over for Griese, who broke his ankle five games into the season, the Dolphins led the NFL in offense, while their “No-Name defense,” composed of tough-nose scrappers such as Nick Buoniconti and Manny Fernandez, allowed the fewest points in the league. They were the first squad with two 1,000-yard rushers and placed seven players in the Pro Football Hall of Fame, along with Shula, whose 347 victories and six Super Bowl appearances likely will never be equaled.

Obama conceded it was “a little unorthodox” to pay tribute 41 years after the fact but explained, “I wanted to be the young guy up here for once!” And he fingered himself among the guilty in not always giving the 1972 Dolphins their due, confessing that he proclaimed the 1985 Chicago Bears “the greatest team ever” when he hosted them in a similar make-up-call celebration at the White House.

Obama noted that the 1985 Bears lost only once. But before he could finish his thought, the 83-year-old Shula chimed in.

“To what team?”

The Miami Dolphins, of course. And the East Room audience erupted.

“You’ve made your point,” Obama said with smile.

To drive his point home further, Shula said he hoped Obama would enjoy reflecting on that Bears’ defeat each time he gazed upon the autographed Dolphins jersey that the team gave him Tuesday, bearing the No. 72 and “UNDEFEATED” across the back. And the coach rose from his motorized scooter to stand alongside the president, who displayed the jersey as cameras flashed.

United four decades later

They had come to Washington from all corners of the country, with Csonka, who spends half the year in Alaska, traveling farthest. The Dolphins’ billionaire owner, Stephen Ross, 73, a Mitt Romney supporter in the 2012 election, paid everyone’s way and joined them for the ceremony.

Along with Shula and his wife, they gathered for dinner Monday at a hotel near the White House. What was striking, apart from their diamond-encrusted Super Bowl rings, was the players’ closeness and affection for one another as they traded bear hugs and belly laughs.

Four decades is a long time. But it had taken nearly that long for Shula and running back Jim Kiick to end their spat over the coach’s decision to split Kiick’s playing time with Mercury Morris. And it had taken nearly as long for the rest of the team to forgive Yepremian’s blunder that nearly cost them Super Bowl VII and, with it, the perfect season.

The Dolphins had held the Redskins scoreless until just over two minutes remained in the game. Yepremian lined up to kick a field goal that would have made the score 17-0, but the Redskins’ Bill Brundige blocked the kick. Yepremian was first to the ball, but instead of flopping on it, he tried to throw a pass. It was disastrous, landing in the arms of cornerback Mike Bass, who ran it back for a touchdown, turning a rout into a nail-biter.

“We threatened to kill Garo if we lost the game,” Kiick recalled. “Here’s a guy that had a hand not big enough to palm a tennis ball, and he’s trying to throw a football!”

Today, the 5-foot-8 Yepremian proudly points out that he leads all NFL quarterbacks in Super Bowl passer ratings, with one attempt that went for a touchdown — alas, to the wrong team.

It’s one of many Dolphins records not likely to be replicated.

Said Griese: “We’re proud of our record. But if somebody goes through a season without losing a game, they’ll just tie our record. And we’ll shake their hands, pat ’em on the back and say, ‘Welcome to history!’ ”