Several offers to go abroad appeared and the player chose to move to Switzerland, signing a contract with FC Winterthur.

[4] After the season Rimkus moved to Cyprus, signing a half-season contract with the Cypriot Fourth Division club Finikas Ayias Marinas Chrysochous.

[5] In July 2011 he returned to Latvia and signed a contract with the Latvian Higher League newcomers FC Jūrmala.

In March 2012 Rimkus was signed by the Latvian Higher League newcomers Spartaks Jūrmala, but after just playing one match he was released.

Despite Rimkus scoring a goal in the promotion/relegation play-offs, his team lost to FS METTA/Latvijas Universitāte 5–2 on aggregate and failed to secure a place in the Latvian Higher League for the 2014 season.

[10] Aged 40, he scored four goals in the first three league appearances for the club, but then left the team turning to playing indoor football.

Before the start of the 2016 Latvian First League season Rimkus returned to association football at the age of 42, joining Skonto FC.