2011-12: Ramsey participated in the Upper Midwest Elite Hockey League in the fall and played 28 games for Minnetonka High School as a sophomore. He had two assists in six games in the Elite league and scored 5 goals with 5 assists in 13 games for the Metro Northwest team in the UMEHL's development league. Ramsey scored 8 goals with 14 assists and had 6 penalty minutes for Minnetonka. The Skippers finished 24-4, losing to eventual Class AA state champion Benilde-St. Margaret's in the Section 6AA championship game.
2012-13: Ramsey was the fourth-leading scorer for Minnetonka in his junior season despite missing three games for the Skippers. He scored 9 goals with 18 assists and was +23 with 6 penalty minutes in 24 games. Ramsey skated for Team Northwest in the UMEHL along with Minnetonka teammate Tommy Vannelli (STL) — a senior defenseman for the Skippers and a Minnesota recruit. Minnetonka finished 19-7-1; losing to Wayzata 5-1 in the Section 6AA semifinals.
2013-14: Ramsey left Minnesota — foregoing his senior year of high school hockey — to skate for the Penticton Vees in the Junior A British Columbia Hockey League. In November he committed to playing college hockey at Minnesota in either 2014-15 or 2015-16. Ramsey played in the 2013 USA Hockey/CCCM All-American Prospects game and was ranked 151st amongst North American skaters in Central Scouting's mid-term rankings prior to the 2014 NHL Draft.