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Warming up for her match while watching Roddick on TV, Serena Williams said she was overcome with emotion. She was in the same situation — next up in Arthur Ashe Stadium — when Andre Agassi gave his equally poignant farewell speech to the fans back in 2006.

“It’s the end of a great player, a legendary player,” Williams said. “Definitely, I was upstairs thinking, ‘Gosh, last time this happened was Andre Agassi. How many more of these do I have to sit through?’ It was great.”

If the moment bothered Williams, it didn’t show. The No. 4 seed overpowered No. 12 Ana Ivanovic 6-1, 6-3 to set up a semifinal against 10th-seeded Sara Errani, who beat her Italian doubles partner, Roberta Vinci, 6-2, 6-4.

The other women’s semifinal will pit top-seeded Victoria Azarenka against No. 3 Maria Sharapova, who returned to her rain-suspended match with a 4-0 deficit but defeated 2007 Wimbledon runner-up Marion Bartoli 3-6, 6-3, 6-4.

Berdych opened his lead over Federer by taking the first-set tiebreaker 7-1. From there, he kept a firm grip on the match, save his stumble in the third set.

“Probably there was not, well, not a bad spot,” said Berdych, who has never won a Grand Slam tournament. “Of course, I lost the third set. But, you know, I cannot count on beating Roger in straight sets and not getting in any trouble.”

Maybe the biggest trouble came in the fifth game of the fourth set when he took an awkward tumble to the court and fell on his right hand, the one he holds the racket with. But on a night when everything went well, there was nothing more than a scrape — nothing to prevent him from finishing up a win in which he played well and Federer couldn’t harness his forehand, committing 24 unforced errors from that side.

He hadn’t played since Saturday, thanks to a walkover he received when Mardy Fish withdrew with health problems. But this year’s Wimbledon champion and silver medalist at the Olympics was not in the mood for excuses.

“Once, I had six and a half days off and I ended up winning Wimbledon,” Federer said. “I don’t think this was the issue tonight.”

Meanwhile, Roddick simply found himself up against a better player. He had beaten men ranked 43rd and 59th since announcing his retirement, but del Potro, the 2009 champion, offered a completely different kind of challenge.

At 6-foot-6 with a flat forehand that he was angling off at will, the 2009 champion here turned things around in the second set. Gaining more traction on Roddick’s once-all-powerful serve, that still maxed out at 135 mph Wednesday, del Potro whipped a cross-court forehand return right at Roddick’s feet on set point.

Del Potro’s momentum continued when he broke to begin the third set, and in the fourth, he broke early, then served out the match.

“No one really wants to be on the opposite side, to be the one who retires someone,” del Potro said. “Andy is that kind of player everyone wants to keep playing forever.”

But nothing lasts forever, and Roddick was very much in touch with that coming into this tournament.

He recalled his first trip to Flushing Meadows, back when he was 9. That was 1991. Jimmy Connors was making his memorable run to the semifinals at age 39.

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