Rämö was drafted by the Tampa Bay Lightning in the sixth round, 191st overall, of the 2004 NHL Entry Draft. A product of the Pelicans organization based in Heinola, Rämö made his SM-liiga debut in the 2003–04 season with Pelicans after the team had lost their chance at the playoffs. In the next season, he played 26 games with Pelicans, later signing a contract with HPK for the 2005–06 season. During the campaign, Rämö shared goaltending duties with Miika Wiikman, putting up excellent statistics and en route to the team's SM-liiga championship. Rämö also represented the Finland junior team at the 2006 World Junior Ice Hockey Championships as the back-up goaltender to Tuukka Rask. After HPK's championship victory, Rämö signed a two-way contract with Tampa Bay. Playing in the American Hockey League with the Norfolk Admirals, Tampa's top minor league affiliate, he made his NHL debut on 2 December 2007 against the Ottawa Senators, replacing Johan Holmqvist. On 19 December, Rämö was again called up by the Lightning. The next day, he won his first career NHL start in a game against the Toronto Maple Leafs, which finished 2–1. He went on to record 7 wins and 11 losses in the 2007–08 season. in 2011. After the Lightning signed NHL veteran Olaf Kölzig as the backup goaltender to Mike Smith, Rämö began the 2008–09 season with Norfolk. He was recalled multiple times by the Lightning throughout the season and finished the year playing 24 games, though he posted just 4 wins. With the prospect of another return to the AHL for the 2009–10 season, on 23 June 2009, Rämö signed a two-year contract with Russian team Avangard Omsk of the Kontinental Hockey League. On 16 August 2010, Rämö's NHL playing rights were traded to the Montreal Canadiens in exchange for goaltender Cédrick Desjardins. In January 2011, Rämö, for the second consecutive year, was selected to be the starting goaltender for the Eastern Conference in the KHL All-Star Game, collecting more fan votes than any other player in the league. However, he was unable to participate due to an injury. On 12 January 2012, Rämö was traded to the Calgary Flames in exchange for Rene Bourque, Patrick Holland and a second-round pick in the 2013 NHL Entry Draft. On 5 July 2013, Rämö signed a two-year, $5.8 million contract with Calgary, paving the way for his return to the NHL. Ahead of the 2013–14 season, during the pre-season, he won the job to replace the retired Miikka Kiprusoff as Calgary's starting goaltender over Joey MacDonald and Reto Berra. Rämö recorded a 15–9–3 record during the 2014–15 season, splitting duties with the newly-acquired Jonas Hiller, though Hiller started more games and also started in the 2015 Stanley Cup playoffs. Rämö was not called into action by the Flames until he replaced Hiller early in Calgary's Game 6-clinching Western Conference Quarterfinals victory over the Vancouver Canucks. After Hiller's sub-par performance in Game 1 of the subsequent Conference Semifinals against the Anaheim Ducks, Rämö would start the remainder of Calgary's playoff games, though the Flames eventually lost the series in five games. He finished the playoffs with a 2–3 record and a 2.86 goals against average. On 1 July 2015, Rämö signed a new one-year contract with Calgary reportedly worth $3.8 million. He struggled early in the season and was sent down to the AHL. However, after being called up after an injury to Hiller, Rämö played most of Calgary's games until a serious knee injury suffered in a game against the San Jose Sharks ended his season. Having returned to health, as a free agent into the 2016–17 season, Rämö signed a professional try-out contract with the AHL's Toronto Marlies on 6 December 2016. On 7 February 2017, having played three games with the Marlies in which he remained winless, he was released from his PTO contract and returned to Finland to continue his recovery to full health. In the 2018-19 season, Rämö was contracted for a second stint with Russian club, Avangard Omsk of the KHL, however injury ruled him out for the entirety of the season without featuring for the club. As a free agent in the 2019–20 season, Rämö signalled his return to health in agreeing to a one-year contract with Swedish club, Djurgårdens IF of the SHL on 4 October 2019. Signed as an injury replacement, he agreed to an initial break of contract after six weeks if his injuries re-occur.
