European Baseball Championship
Markwell represented the Netherlands at the 2004 Summer Olympics in Athens, where he and his team finished sixth. Markwell was also named to the Dutch roster for the 2005 European Baseball Championship, 2006 World Baseball Classic, 2006 Intercontinental Cup, 2007 European Baseball Championship, 2008 Summer Olympics, 2009 World Baseball Classic, 2010 European Baseball Championship, 2010 Intercontinental Cup, 2011 Baseball World Cup, 2013 World Baseball Classic, 2013 World Port Tournament, , 2014 European Baseball Championship, 2015 World Port Tournament, 2015 WBSC Premier12, 2016 Haarlem Baseball Week, , and the 2016 European Baseball Championship. He played for Team Netherlands in the 2019 European Baseball Championship, and at the Africa/Europe 2020 Olympic Qualification tournament in Italy in September 2019.