And Murray served rather well himself, too.
Still seeking his first Grand Slam title, Olympic champion Murray reached the quarterfinals at an eighth consecutive major tournament by beating 15th-seeded Raonic 6-4, 6-4, 6-2 on Monday night.
The third-seeded Murray converted 4 of 12 break points and never faced one. After weathering six aces across Raonic's first three service games, Murray only allowed eight the rest of the way.
"You start to see things after a few games. He started serving a lot of big serves. I was just trying to react as quickly as possible," Murray said in an on-court interview at Arthur Ashe Stadium. "Sometimes they fly past you, sometimes you get a racket on them -- and I got a racket on them."
Raonic's 14 aces were less than half as many as he accumulated in any of his first three matches this year at Flushing Meadows, when he hit 30, 30 and 29.
"I used a lot of variation tonight. Milos has a huge game, massive serve. I had to guess on some of the serves," Murray said. "I got lucky a few times."
Next for Murray is a match against No. 12 Marin Cilic. Murray leads their head-to-head series 6-1, but his only loss to Cilic came at Flushing Meadows in the fourth round in 2009.
"Really interesting for me. Another big challenge. Andy's obviously playing really well," Cilic said after his 7-5, 6-4, 6-0 victory over 50th-ranked Martin Klizan of Slovakia earlier Monday.
"When I feel well," Cilic added, "I feel I can match up with anybody."
Murray probably thinks the same way, especially with the confidence boost he picked up with his gold medal last month.
He's yet to win the last match at a Grand Slam tournament, though: Murray and his coach, Ivan Lendl, are the only men to lose their first four major finals.
Murray only had played once before against Raonic, who was trying to become the first Canadian man in a major quarterfinal in the Open era, which began in 1968.
Berdych wrapped up his match at about the same time Federer's opponent, Mardy Fish, withdrew for undisclosed health reasons.
"At least good that I didn't stay that long on court, that I was able to save some energy, as well," Berdych said.
Berdych needed exactly two hours to beat Almagro and make his first U.S. Open quarterfinal. Berdych finished with 39 winners and only 16 unforced errors.
"It will be a tough match against Tomas," Federer said in a statement. "We have played many times in the past and he has always been a tough opponent. I will have to continue to serve well and dictate the points."
Berdych is 4-11 lifetime against Federer, but 3-3 in the last six matchups, including a win at their last Grand Slam meeting, the quarterfinals of Wimbledon in 2010.
Information from The Associated Press was used in this report.