But both 30-somethings admitted at the French Open they still get a shiver of fear before their opening matches at one of the big four two-week events.
"I wasn't nervous going into the match. But there's always that little bit of feeling that if you don't feel well, if the opponent plays great, you could lose early," said Federer after his 6-2 6-4 6-2 defeat of Slovakia's Lukas Lacko.
"It's more just like those hints of fear - maybe yesterday, maybe this morning at one point, just for five seconds, 'Oh, I really hope I don't have to pack my bags today', that kind of feeling."
In his early days, the famously cool Swiss says he was often badly affected before and during big games.
"I have had the shakes and ended up losing the match. I don't think I lost because I was nervous necessarily, but just because of the circumstances," added the 2009 Roland Garros champion.
"During a match, you have a very elevated pulse and you get the shakes sometimes, and you don't know why that is. Sometimes your legs just freeze, so you try to stay in movement.
"I was probably very nervous for the (Pete) Sampras match at Wimbledon (in 2001), because it was my first time on Centre Court, my first time against Pete.
"There I remember the cold hands, nervous, the pulse. Just feeling like this is not the usual match, that kind of thing. Then I have had it probably on some other occasions like the first final, or the first title I won.
"Just those moments when it happens for the first time - it's like the first time you have to make a speech or walk up to a girl and talk to her because you like her kind of thing. It's just when you're not used to it, I think that's what freaks you out the most."
But age, and 16 years on tour, means Federer knows how to damp down any negative thoughts.
"I don't get too worked up about it, because I know it's a long match, maybe, potentially ahead of me and it's not a sprint to the finish line, it's more of a marathon," he explained.
"Today with my experience I'm more laid-back going into a tournament, going into a first round of a grand slam."
Serena, the defending champion at Roland Garros, is also not immune to butterflies in the stomach, but the fighter in her always tries to feed off that nervousness.
"I think in general I always have a little bit of nerves and just I try to harness them and put it in the right place. I was extremely nervous last year here in the final," the American, who beat Maria Sharapova to win her second French Open title last year, said following Sunday's 6-2 6-1 win over Alize Lim.
"The whole match I could barely get there. I was really, really, really nervous. Then also the U.S. Open (where she also won the title) I was nervous.
"I think it's nice to have a little bit of that, because it means that you still have a passion for it. You still have this inside feeling that you want to do really well or else the nerves wouldn't be there."
REUTERS / EUROSPORT
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