Neither has lost one yet and tomorrow, the two men will bid to set up what is expected to be a classic semi-final.
Murray takes on Jeremy Chardy of France, about as good a draw as he could have hoped for, having yesterday cruised past another Frenchman, Gilles Simon, 6-3, 6-1, 6-3 while Federer, the second seed, meets Jo-Wilfried Tsonga, having outclassed Milos Raonic of Canada 6-4, 7-6, 6-2 last night.
Both men are too experienced to let their straightforward starts make them think the next one will be easy but equally they will have been delighted that they have avoided the kind of five-hour marathon that the defending champion Novak Djokovic came through in round four.
Djokovic was scheduled to play Tomas Berdych in the quarter-finals this morning but, even if he gets through that one, the cumulative effect could be disastrous in the long run. Murray admitted he would rather be in his position than Djokovic's even if he fell short of saying he had an advantage over the world No.1.
"Some slams I've started off really, really well and some I had some tough patches in," Murray said, shortly after finishing off Simon, who was still exhausted from his epic win over Gael Monfils in the round before. "Sometimes at the Australian Open I've started really well and got through to the second week without dropping a set. It doesn't really matter; Roger hasn't lost a set either yet and I'm sure he will be happy with where he's at. You just have to wait and see whether you're ready to up it when the time comes but I hope I will be ready."
Since the arrival of Ivan Lendl as his coach just more than a year ago, Murray has taken most things in his stride and said issues like scheduling were much easier to cope with now. Where once he might have panicked, now he just accepts and moves on.
What he would like, though, is a night match to get used to the often cooler conditions in the evening. The semi-finals and final will both be played in the evening but his quarter-final may well still be in the daytime, with Federer and Tsonga perhaps more of a box-office draw.
"Ideally it would be nice to get a match in the evening but, if not, you just get on with it," he said. "Sometimes the schedule works well for you and sometimes it doesn't work out perfectly.
"I've had scenarios like that at the US Open where it worked in my favour. Wimbledon didn't necessarily work in my favour this year, or last year, and the first US Open final I played, it didn't work in my favour. But you don't dictate the schedule, you just try to play and deal with everything as best you can.
"When you do play in the evening, the conditions feel fine to play in. Just the thing you need to get used to is the timing of the ball and the speed of the courts. They change when it's dark."
Simon had warned that he was unlikely to be in any kind of shape to give Murray a real fight and so it proved. The Frenchman had been left exhausted after his five-set win over Monfils, a match that contained an incredible number of rallies of over 40 shots, with one 71-shot rally taking both players' breath away.
Keeping his concentration was the only concern for Murray but he got the job done quickly, conserving his energy for the battles ahead. The first of those is against Chardy, ranked No.37 in the world but a man who beat Murray in their most recent match, in Cincinnati last summer. That came soon after the Scot's Olympics victory, though, so perhaps that played a part.
Like so many of the Frenchmen on Tour, Chardy plays with huge flair, with a big serve and an explosive forehand. Based at the Mouratoglou Academy on the outskirts of Paris, he is coached by 27-year-old Kerei Abakar, a man whose experience is dwarfed in comparison to Lendl.
"What can I say? I only have big respect for this guy [Lendl] but I'm not going to feel weaker," Abakar said. "I will just try to give my maximum strength to Jeremy. But I won't feel inferior to them. They are strong. Everybody knows Andy is a top-four player. We know that Ivan Lendl won many grand slams. But I'm going to fight with him, that's it."
If Murray had it easy, then Federer went into his match with Raonic knowing he would need to play well to get through. So he did. The Swiss produced a superb display to win in straight sets and reach his 35th straight grand slam quarter-final.
Federer has not even dropped his serve in the entire tournament, not bad going, considering he arrived in Melbourne without playing a warm-up event.
"Especially early on in the season, not having played any tournaments before, this is obviously a great thing I have going," he said. "But I go into matches expecting to be broken. The more you talk about it, the more so you're going to be broken. So I'm just happy to drop that subject and sort of move on."