Savėnas represented Lithuania at under-21 level before establishing himself as a regular player in the Lithuania national team.
In the 2005 season Savėnas became LithuanianA Lyga top scorer with 27 goals and was voted best player in Lithuania, receiving 177 from 200 votes. Following the 2013 season Savenas was voted as the Daugava Rīga best player of the season.[2] In 2014, he was the club's top scorer with 10 goals in 30 appearances.