MELBOURNE, Australia » After Madison Keys walked off the court from the biggest match of her young career, she received quite a compliment from her celebrated opponent.

The opponent was No. 1-ranked Serena Williams, who won their semifinal at the Australian Open on Thursday after a tournament that might be remembered as the one where a new American star was born.

Williams does not say things like this lightly or very often: "I think she can be the best in the world." Then she added, for emphasis, "The way she played today, I definitely think she has potential to be No. 1 — and win Grand Slams."

Until now, Keys had never made it past the third round of a major. But the Australian Open marked many firsts for the 19-year-old American.

"Did I think it was going to happen here? Not particularly. But I’m very happy it did," said Keys, who won many fans with her sense of humor, big smile, a humble self-confidence and her very good tennis.

During the tournament, she talked about how she’ll save most of her $510,000 prize money but allow herself one indulgence, possibly a Louis Vuitton handbag. She shared the advice of her new coach Lindsay Davenport, a three-time Grand Slam winner, who told her to stay off Twitter and keep focused on tennis for the tournament. That and other advice clearly paid off.

For the first time, Keys crossed the psychological boundary of entering into the second week of a Grand Slam.

On her way to the semifinal, she beat two-time Wimbledon champion Petra Kvitova in the third round and seven-time Grand Slam winner Venus Williams in the quarterfinals to set up back-to-back matches with the Williams sisters, a challenge that held special significance for Keys who had idolized both as a child.

Her ranking will improve from No. 35 into the top 20 as a result of reaching the semifinal.

Playing Williams marked the first time Keys had ever faced a No. 1-ranked player — and she put the 18-time major winner to the test.

Their semifinal on a breezy and chilly afternoon was the most-hyped women’s match of the tournament so far: the up-and-coming prodigy against one of the greatest champions of all time. This time around the champion won, 7-6 (5), 6-2, but the score does not tell the story.

Keys showed no fear, enormous grit, extremely powerful hitting, a big serve and was calm enough in the big moments to save seven match points.

"This week has definitely shown me that I can play the top players, and I can do well against them," Keys said. "I can play the No. 1 player in the world in a pretty close match."

The crowd at Rod Laver Arena ooohhed and ahhhhed as the ball rocketed back and forth during rallies with intense speed and force from both baselines.

Keys described the quality of Williams’ shots like this: "It comes hard; it comes deep… she’s one of the few who can hit like that."

Interestingly, Williams described Keys’ hitting precisely the same way: "She hits a very, very hard ball, but she also hits it very deep," Williams said. "I wasn’t ready really for that."

Keys was asked what she thinks makes her a good tennis player, and she described the fighting spirit that was evident on court.

"For me, even this week, as great as it is, I still want more," she said. "For me, it’s just never being satisfied with what I’ve done and always wanting more and more."

When Keys reached the quarterfinals, she drew laughter at her post-match press conference by describing her state of mind with an emoji.

"You know, the one that she’s in a salsa dress dancing. That would be me right now," Keys said after the fourth round.

And so, after the semifinal loss, which emoji sums up her two weeks in Melbourne?

"I think pretty much just the smiley face," she said with a smile. "Can’t go wrong with the plain old smiley face."