As Ivo Karlovic reached into his bag for his sunglasses, it was tempting to imagine that he needed them to block the brilliance of the white light that emanated from Roger Federer.

The No 2 seed was neither hot nor bothered as he faced one of the most powerful serves in the game with a calm equanimity. It was unnerving. The Swiss performed miracles while looking as though he was starring in a washing powder advertisement.

What Federer can conjure ought not to surprise anyone, but he jolted the Centre Court crowd as early as the fourth game of the first set in his 6-3, 7-5, 7-6 victory by breaking, with huge panache, the scary Karlovic serve — and no one saw it coming.

The Croat had seemed relaxed and confident and his first service game was spectacular. He opened with an ace, then delivered an unplayable serve, a more or less unplayable serve and finished it all off with a truly unplayable one. The heads bobbed as the thought hit everyone: this was going to be dominated by tie-breaks.

Then Federer, when next asked to deal with Karlovic’s serve, unpicked it as calmly and precisely as if he had been asked to untie a toddler’s shoelace. Be clear that this was no ordinary serve. Karlovic, until facing the white light, had won all 79 of his service games at the championships and faced only four break points. Federer’s timing was a masterstroke and Karlovic never really recovered. The Swiss did not have to ping back every 138mph serve, but knowing that he had done and could so again took away his opponent’s only weapon.

The contest was not everyone’s idea of entertainment but was fascinating in its own way.

“It’s not fair to call him boring,” Federer said. But it took until the fourth game of the second set before the match produced a rally of any consequence. It felt incongruous, as if both players had suddenly decided that they needed a bit more of a warm-up. And why on earth should Karlovic want to elongate the points against a player of Federer’s calibre? The few rallies played tended not to be won by him and the only piece of effective creativity away from his serve came halfway through the third set when he produced a forehand passing shot on the Federer serve.

Federer now faces a semi-final against Tommy Haas, who took the first two sets off him in the fourth round at Roland Garros. “As we saw in Paris, it was brutal,” Federer said, but he was not quaking. “I think on grass all my strength becomes even better. I become so much more dangerous.”

Federer’s victory takes him to his 21st consecutive grand-slam semi-final as he bids to make history by winning 15 grand-slam titles. “It means a lot to me — 21st in a row,” he said. “Just being so consistent for so long. It’s quite a streak I’m on and I’m happy it’s still alive. It’s amazing. Means the world to me. Let’s see what happens now.”

Clearly Federer has an inkling as to what will happen now. If he didn’t, he would not be the fearsomely successful athlete who is greatly admired. He withstood, he felt, the brutality of Haas in Paris with the application of self-belief, saying: “I stayed calm.”

Should Andy Murray reach the final to face Federer, the British No 1 should probably not bother asking Karlovic for insight. The Croat was completely stunned by Federer’s response to his serve. “He returned unbelievable,” Karlovic said. “He is better than everybody else.”

The design on Karlovic’s shirt made it look as if he was wearing a backpack. As the match progressed, that impression grew; facing Federer in this sort of form must be like having to play in the heat with a rucksack full of rubble on your shoulders.

And still, Federer is not even slightly distracted by his wife’s pregnancy. “Going through semi-final, finals days, Mirka being pregnant, you know, it feels good,” Federer said. “She’s been very supportive.”