Cardinals coach Rick Pitino brought the Midwest Regional championship trophy when he visited Ware, who remains hospitalized after surgery to repair a gruesome fracture in his right leg.
"He was real excited about (the trophy)," Pitino said after visiting Ware again Monday morning. "I said to him, 'You want me to bring it back or stay with you?' He said, 'It's staying with me.' I said, 'All right, just make sure you don't lose it.'"
During a 2-hour surgery Sunday night, doctors reset Ware's broken tibia and inserted a rod into the bone. Because the bone broke through the skin, Pitino said doctors are monitoring Ware to make sure no infection develops. If there are no complications, he should be released Tuesday.
The Cardinals plan to leave for the Final Four in Atlanta on Wednesday night, and Pitino said they expect to have Ware with them. Ware is originally from New York City, but he moved to the Atlanta area before high school.
"He gets to go home, be with his family and be with us on the bench," Pitino said. "He's in very good spirits and anxious to get out of the hospital and get back with the guys."
Ware's right leg snapped in the first half of Sunday's Midwest Regional final when he landed awkwardly after trying to contest a 3-point shot. The horrific injury devastated his teammates, and several fell to the court crying. Chane Behanan, Ware's best friend on the team, had to be helped to his feet.
But before Ware was wheeled off the court on a stretcher, he repeatedly urged the Cardinals to "just go win the game." The Cardinals did, beating Duke 85-63 to reach their second straight Final Four, and they said afterward there was no way they could have let Ware down.
"Right before the surgery, when he was able to watch the players at the press conference, the nurses and doctors told me that was the first time he broke down and cried, when the players were talking about him," Pitino said.
Ware's injury dominated social media Sunday night, and Pitino said the sophomore guard has been moved by all the messages of support. Joe Theismann, whose NFL career was ended by a horrific broken leg in a Monday Night Football game against the New York Giants, has called Ware, Pitino said. On Sunday, Theismann tweeted, "Watching Duke/ Louisville my heart goes out to Kevin Ware."
Television analyst Greg Anthony also called, and Pitino said Duke coach Mike Krzyzewski called him Monday to see how Ware was doing.
"A lot of really positive calls that are making him feel good," Pitino said.
Pitino and his son, Richard, who recruited Ware while he was on his father's staff, were at the hospital when the sophomore guard got out of surgery and went back Monday morning. Ware's girlfriend stayed with him overnight, and his mother and her husband arrived Monday.
"She just needed to see him this morning," Pitino said. "She was crying all night. Once she gave him a hug this morning, she was fine. Everything is good right now."
Ware was back on Twitter early Monday, thanking everyone from Kobe Bryant to Lil Wayne and other well-wishers. He wrote that he would be back "by next season" and quipped that he "should of blocked that shot." Among his visitors was NCAA President Mark Emmert, spokeswoman Stacy Osburn said.
"He was there to see how the student-athlete was doing and offer words of encouragement," she said of Emmert.
Kenny Klein, Louisville's sports information director, tweeted a picture of Ware on crutches Monday. Richard Pitino, now the coach at Florida International, posted photos of Ware with his family and with the championship trophy.
While some have speculated that Ware could have had a previous stress fracture that left him predisposed to such an injury, Pitino discounted that, saying there was "nothing prior."
"Basically his leg went one way and his shoe went another and the bone split," Pitino said. "There's no preexisting thing that makes it do that."
Ware's injury is similar to the one suffered by running back Michael Bush, who also played at Louisville. Bush recovered from the injury and has had a productive NFL career with Oakland and Chicago.
"It will be a long recovery," Pitino said. "But we expect him to make a full recovery."
AP Sports Writer Michael Marot in Indianapolis contributed to this report.