Just hours earlier he had won his record-breaking eighth Wimbledon title. It also happened to be the day after Liu had become the first American female in 25 years to capture the singles title at Wimbledon's Junior Championships.
The 17-year-old from Thousand Oaks, California, walked up to the 19-time Grand Slam winner at the champions' dinner while repeatedly saying to herself, "Stay calm, stay calm."
Federer looked up at her as she approached, and an instant smile appeared on his face. He recognized Liu from her final match.
"Congratulations, Claire," Federer said. "I hope you're having a good evening."
Liu recollects saying, "Thank you, Roger," at least 10 times during their one-minute interaction.
She mustered up her courage and asked him if he would take a picture with her. He smiled and said yes. Taylor Johnson, Liu's doubles partner, took a picture of Liu smiling radiantly next to the dapper Federer.
As Liu walked back to her seat, she felt as if she were floating away from the ballroom, unable to believe what had just happened.
"Did Federer really recognize me?" she kept asking herself.
That was the moment she knew she had made it. When one of the greatest tennis players of all time recognizes you for your performance, it means you've done something right, she thought to herself.
In 2010, Liu was in the stands of Wimbledon's No. 1 court when Kristyna Pliskova won the junior title. Who knew Liu would be the one to lift the trophy seven years later.
The chocolate mousse on her plate suddenly tasted so much better.
"I AM TERRIBLE. I am junk."
That was Liu's opening remark to her new USTA coach, Chris Tontz, after losing yet another match in February. She was in tears. She had been unable to pull off victories early in the year and was frustrated with herself.
What she didn't know at the time was this: She would win two ITF tournaments -- in Naples and Caserta -- finish runner-up in the Junior French Championships and bring home the Wimbledon trophy in the next five months.
When Tontz started coaching Liu, he had one immediate goal: to build her confidence. Liu had a powerful game with a big serve, a seething backhand and the ability to finish points at the net. All she needed was belief in herself.
Tontz asked Liu to tell him something positive about herself that first session. "It took her four days to tell me one good thing about herself," Tontz said.
She eventually told him quietly that she was the youngest person to win a pro tournament since Anna Kournikova (1996) when she won in Orlando at age 14 in 2015.
"Now, she tells me four good things about herself every day," Tontz said.
Tontz realized that Liu was putting a lot of pressure on herself by taking a results-oriented approach. She needed to enjoy waking up every morning to go the gym and to train. She needed to enjoy the process.
Slowly, he noticed her smiling more. He could see the transformation in her game. He felt wonderful to be a part of it.
The moment Liu defeated fellow American Ann Li in the Wimbledon final and slid on her back with tears in her eyes, another person was crying on a couch in California -- Chris Tontz.
LIU LOVED PLAYING tennis with her parents from an early age. Her parents noticed her zipping serve and a solid backhand when she was just 4 and enrolled her in a camp close to their home in Thousand Oaks.
When she was 9, she received an invitation to train with the USTA.
"She loved the sport, and we wanted to do everything we can to make sure she got the best facilities," said Wen Liu, Claire's mom.
Liu has been training at USTA's facility in Carson, California, ever since. She is now a distance-education student at Century Academy High School in Thousand Oaks, where she will be a senior in the fall.
Rodney Marshall, a USTA strength and conditioning coach, recollected how when Liu first arrived, she would grab his arm tightly and walk alongside him wherever they went.
"Now she has blossomed into this amazing, strong lady," Marshall said.
At Carson, Liu trained alongside Madison Keys and Sam Querrey. She watched Sloane Stephens transition from junior tennis to the pro ranks. She watched Mardy Fish come back after a knee injury and climb to No. 7 in the world. She had lunch sessions with pro athletes and, even though she was a preteen, she started thinking like them and training like them, Marshall said.
Her teammates loved her team spirit. They enjoyed playing with her in doubles and training against her in singles.
"It's hard to beat her in singles because she is good at everything -- serving big, volleying and finishing off points on the net -- and it's great to play doubles with her because she will serve big and set up the point for me to finish off," Johnson said.
Without realizing it, Liu grew tougher. At age 15, five months after she'd won the Orlando ITF event, she reached the final of the 2015 US Open qualifier. She was making a strong transition from junior to pro tennis.
Many young tennis players give up junior events once they start winning $25,000 ITF tournaments, but Liu's decision to go back and forth is helping a lot with her adjustment to the next level, said Martin Blackman, USTA general manager of player development.
"She can play free in the pros because she's got no pressure," Blackman said. "In the juniors, she is one of the best in the world, so she's got a lot of pressure."
LIU HATES LOSING, even during practice. Gena Ball, a USTA coach, recollects a workout session in 2016 when Liu had to do 10 400-meter runs with other athletes. She had eaten a big burrito before the workout, making it tough, but she pulled through (and, Ball said, learned not to eat burritos before workouts).
"She might be dying, but she won't give up," Ball said.
Liu says she has learned a lot from Kim Clijsters' game, the way the Hall of Famer moved on the court and her inspiring calmness.
Off the court, Liu's role models are her parents, who emigrated from China. When she's not training or playing, Liu is at home cooking stir fry or pasta with her sister, and hiking and playing board games with her family.
With the US Open just around the corner, Liu's coaches and teammates are confident that she has it in her to win another junior Grand Slam. But they also have another dream for her: to get a wild card into main-draw qualifiers.
"If she does, she has the ability to go up to round three of the main draw," Tontz said.
Liu's next goals are to break into the top 200 of the WTA women's ranking this year and make it to the main draw of the Australian Open in 2018. She is ranked No. 291 in the world at the moment. She has another year to decide whether she'll turn pro immediately after graduating high school or play a couple of years of NCAA tennis first.
The ultimate dream for Liu's USTA coaches would be to see her get to the women's Wimbledon final and win the title. But they also want her to enjoy the process.
"A lot of athletes get to pro level and they lose that spark, but I want her to continue to enjoy it like I know she does right now," Ball said.