LONDON—Think of them as the 20th-century kids. Roger Federer and Venus Williams both made their Wimbledon debuts back in the now-mythic 1990s, as talented but raw 17-year-olds.

Despite high expectations and obvious skills, neither made it out of the first round. In 1997, Venus lost to Magdalena Gryzybowska of Poland in three sets. “I was so nervous in my first match here, it was a total disaster,” Williams said with a laugh yesterday. “Poor young V.” Two years later, Federer, a wild card, lost to Jiri Novak in five sets.

Neither let those setbacks discourage them. There are few tennis players who don’t love Wimbledon, but Federer and Venus identified themselves with this place and this event right from the start, and every year since they’ve made winning it their first order of business. The same is true for the Olympics, which they made cool for tennis players to care about. Venus and Federer were from the first generation of pros who grew up watching tennis at the Games, and they were the first to fully embrace it when they had the opportunity. The thrill of their first Olympics, which came in Sydney in 2000 for both of them, never wore off. Venus and Federer have always been, first and foremost, tennis enthusiasts.

The thrill of winning Wimbledon has obviously never worn off for them, either. In 2000, Venus won her first title here; in 2001, Federer upset seven-time champ Pete Sampras in the fourth round in the first undeniable sign of his potential. Venus would go on to win Wimbledon five times, and Federer would tie Sampras with seven.

Until this week, those numbers appeared to be set in stone. Williams, now 37, won her last Wimbledon as a wide-eyed 28-year-old in 2009; Federer won his last in 2012, at 30, an age that used to be seen as a Rubicon for tennis players—to go past it meant to go into terminal decline. Now, in a remarkable co-story—a story for the aged, as it were—they’re both back in the final. For Federer, it’s his 11th in 19 trips to Wimbledon; for Venus, it’s her ninth in 20 trips. Federer is the oldest man to reach the final here since Ken Rosewall in 1974; Venus is the oldest woman since Martina Navratilova in 1994.

Each has played this tournament with a similar sense of resolve and tenacity; they’ve been determined not to let the chance slip, and as Grand Slam champions tend to do, they’ve improved with each match.

Venus and Federer have two of the most reliable, and somewhat underrated, serves in tennis history, and it has all started with that shot during this Wimbledon for them. This was doubly true in their straight-set semifinal wins, over Johanna Konta and Tomas Berdych. Down a break point at 4-4 in the first set, Venus uncorked a 106-m.p.h. second serve. Down two break points in the third set against Berdych, Federer fired three aces and a service winner. As Grand Slam champions tend to do, they’ve found something extra when they’ve needed it. At 1-1 in the second-set tiebreaker against Berdych, Federer suddenly let loose with four straight point-winning forehands to break the match open.

For Venus and Federer, it’s about letting instinct—instinct informed by 20 years of experience—take over.

“I feel like it reminded me of the matches I’ve had this tournament on some occasions, you know, there were chances for the opponent,” Federer said. “I was able to come up with the goods when it mattered.”

“I’m just out there competing,” Venus said after beating Konta. “I try to produce whatever I need at the time. There’s no plan or anything like that. I don’t plan. I’m just trying to compete.”

Most people will look at Federer and Venus and wonder how they can physically stay with players a decade, or even two decades, younger than they are. To me, though, what’s surprising and remarkable is what they’ve done mentally this season.

For years, as she got older, Venus struggled in close matches; like Rafael Nadal, she specialized in making stirring comebacks, only to lose in the end. Federer’s problem wasn’t losing close matches so much as it was losing late in Grand Slams after looking like the best player in the tournament for the better part of two weeks. It appeared that rather than slowing them down, age had robbed them of just enough of their confidence and edge to make winning major titles seem beyond their reach. But their Australian Open successes—Federer won the tournament, Venus reached the final—signaled a rebirth for both of them, confidence-wise.

What’s the secret to their success? Not dwelling on how old they are seems to be one. “I’m not thinking about age,” Venus said earlier this week. When Federer was asked about being in the final at 35, he quickly deflected the question by talking about how happy he was to see Rosewall in the Royal Box on Friday.

The other key, of course, is loving what you do. Venus and Federer love tennis like few others have, enough to keep traveling, keep getting on airplanes, keep practicing and keep grinding on tour for 20 years. This, another Wimbledon final, is their reward. But they both know it’s too early to celebrate.

“There’s still a lot to be done,” Venus said on Thursday. “I’m definitely excited. There’s one more match that I’d like to, you know, be the winner of. But I like to take courage in the fact that I’ve been playing well this tournament and this year, and all these moments have led to this.”

“It’s a big deal,” Federer said on Friday. “I love this tournament. All my dreams came true here as a player ...Yeah, unbelievably excited. I hope I can play one more good match.”

Between them they have 72 years, 40 seasons on tour and 12 Wimbledon titles, but Williams and Federer are still talking like rookies. Would you bet against the 20th-century kids this weekend?

—GRAND SLAM WEEK: Watch Wimbledon Primetime on Tennis Channel, and catch up on the other 2017 Grand Slams on Tennis Channel Plus

—Watch encores from the 2017 French Open and Australian Open on Tennis Channel Plus, including matches like the AO Final showdown between Serena & Venus Williams