It's one of the hardest sports trophies to win.

And when each and every NHL playoff tournament ends, there's a particularly poignant moment when a championship team's popular first-timer has the Stanley Cup handed to him for a celebratory skate.

Steven Stamkos was that man for the Tampa Bay Lightning a few months back, following the giddy likes of Ray Bourque, Dave Andreychuk, Doug Weight and many others in the last 20 years.

But there's an equally gut-wrenching moment elsewhere.

Whether it's on the beaten team in the Stanley Cup Final or the losing sides of the other series-ending handshake lines, dozens of other veterans end their seasons and sometimes even careers without ever hoisting the chalice.

That harrowing reality prompted the B/R hockey team to gather again to compose a list of the half-dozen players beyond age 30 we'd most like to get a chance to receive the greatest of all on-ice handoffs.

Take a look at our picks and let us know in the comments who else you deem worthy.

Brent Burns

It's not as if Brent Burns hasn't had things to celebrate.

In fact, the 35-year-old defenseman won the Norris Trophy in 2017, was a finalist for the award two other times and has been an All-Star six times since debuting with the Minnesota Wild in 2003.

He's played more than 1,000 regular-season games, scored more than 200 goals and is only six games away from reaching triple digits in the postseason as well.

But he's never been a part of the ultimate team picture at center ice.

In fact, the mammoth 6'5", 230-pounder has advanced to the Stanley Cup Final just once in 15 NHL seasons, losing with the San Jose Sharks in six games to the Pittsburgh Penguins following the 2015-16 campaign.

The Sharks were one of seven teams that didn't qualify for the modified 2019-20 postseason, just one year after they'd reached the Western Conference finals before losing to the Stanley Cup-winning St. Louis Blues.

Burns is signed through 2024-25 at $8 million a season, so a full-on San Jose rebuild might be necessary if he's to get another shot before he retires.

Henrik Lundqvist

Some players get to the playoffs and don't produce in the same manner as in the regular season.

Henrik Lundqvist is not one of those players.

The 38-year-old Swede has played in 130 career postseason games, posting a 2.30 goals-against average and .921 save percentage—both better than his lifetime regular-season marks—alongside 10 shutouts that are second among active goaltenders behind only Marc-Andre Fleury.

In spite of the numbers, Lundqvist has only had one direct shot at a title, advancing to the 2013-14 Stanley Cup Final with the New York Rangers before falling in five games to the Los Angeles Kings.

He made his last two playoff appearances with the Rangers in 2019-20 before the team bought out his contract. He signed a one-year deal with the Washington Capitals, who won the Cup in 2018 and are in the upper echelon of teams with a chance to win again this season.

Lundqvist's future, though, is in doubt after a lingering condition required open-heart surgery earlier this month.

He said he would not return to the ice with the Capitals this season, and it seems far from guaranteed that another NHL team will call with an offer for a near-40 goalie with potentially serious medical concerns.

Ryan Miller

Here's another nod to the netminders.

No active NHL goaltender has played more seasons without a Stanley Cup than Ryan Miller, now 40, who was drafted No. 138 overall by the Buffalo Sabres way back in 1999.