His performance at the Adidas Superstar Camp earned him a selection to the World All-Star Team.

Following the 2005–06 season, Shermadini was invited to the "Basketball Without Borders" (BWB) Europe camp, conducted at Vilnius, Lithuania, from June 30 to July 3.

[4] In April 2007, Shermadini was invited to the "Nike Hoop Summit" World Select Team.

Unfortunately, he did not play with the World Select Team, due to an injury to his meniscus, which required surgery.

He surpassed his personal best again, although playing only for 12 minutes, by scoring 13 points in a home game against Union Kavala-Panorama, on 15 April 2009.

[7] In June 2012, he signed a two-year deal with the Israeli Super League club Maccabi Tel Aviv.

[12] On May 26, 2021, Shermadini was named the Most Valuable Player of the 2020–21 ACB season after averaging 17.0 points, 5.4 rebounds and a PIR of 22.5.

Following his surgery and rehabilitation, for his meniscus injury that he suffered in 2007; he was invited to the Under-20 Junior National Team of Georgia.

He played alongside teammates, Zaza Pachulia (Atlanta Hawks), Nikoloz Tskitishvili (Teramo Basket), Shammond Williams (Valencia), Viktor Sanikidze (Tartu Ülikool/Rock), Manu Markoishvili (Olimpija Ljubljana), and Vladimir Boisa (Menorca Bàsquet).

In February 2023, Shermadini was on there roster that made Georgia qualify for its first-ever World Cup in 2023.