Heppner was awarded the National Arts Centre Award, a companion award of the Governor General's Performing Arts Awards in 1995. He was made a Member of the Order of Canada in 1999, was promoted to Officer in 2002 and Companion in 2008. He performed at closing ceremonies of two Winter Olympic Games. In Turin in 2006, he sang the Canadian national anthem. Four years later, in Vancouver, he sang the Olympic Hymn. Both times, he mixed English and French. In June 2016, Heppner was made a laureate of the Governor General's Performing Arts Awards, with a Lifetime Achievement Award in Classical Music.