MELBOURNE, Australia — When Mirjana Lucic-Baroni served out her victory over Karolina Pliskova at the Australian Open today, making an unlikely return to the semifinals of a Grand Slam after nearly 18 years, she fell to her knees, placed her forehead on the court and wept.

Few expected her to ever have this chance at a major again. Lucic-Baroni, however, never gave up believing in herself.

It was a heartfelt scene that touched even Serena Williams, her opponent in the semifinals at Melbourne Park, who started her career at the same time as Lucic-Baroni.

“I’m so proud of Mirjana,” Williams said after her 6-2, 6-3 victory over ninth-seeded Johanna Konta. “It’s so good to see her back out and to see her in the semifinals really just is so inspiring for me.

“No matter what happens, someone 34 or older will be in the final and that’s just really awesome.”

Williams, 35, and Lucic-Baroni, 34, will meet Thursday in the semifinals.