Ernst was a foreign fellow of the Estonian Academy of Sciences (elected 2002), the US National Academy of Sciences, the Royal Academy of Sciences, London, the German National Academy of Sciences Leopoldina, the Russian Academy of Sciences, the Korean Academy of Science and Technology and Bangladesh Academy of Sciences. He was elected a Foreign Member of the Royal Society (ForMemRS) in 1993. He was awarded the John Gamble Kirkwood Medal in 1989.
In 1991, Ernst was on an aeroplane flying over the Atlantic when he discovered he had been awarded The Nobel Prize in Chemistry. He was invited into the cockpit, where he was given a radio to talk to the Nobel committee. Here they told him he was being honoured "for his contributions to the development of the methodology of high resolution nuclear magnetic resonance (NMR) spectroscopy".
Ernst was member of the World Knowledge Dialogue Scientific Board. He was awarded the Marcel Benoist Prize in 1986, the Wolf Prize for Chemistry in 1991, and Louisa Gross Horwitz Prize of Columbia University in 1991. He was also awarded the Tadeus Reichstein Medal in 2000 and the Order of the Star of Romania in 2004.  He also held Honorary Doctorates from the Technical University of Munich, EPF Lausanne, University of Zurich, University Antwerpen, Babes-Bolyai University, and University Montpellier.
The 2009 Bel Air Film Festival featured the world premiere of a documentary film on Ernst Science Plus Dharma Equals Social Responsibility. Produced by Carlo Burton, the film takes place in Ernst's hometown in Switzerland. In 2022, another movie about Richard R. Ernst premiered at the Cameo cinema in Winterthur, produced by Lukas Schwarzenbacher and Susanne Schmid. The documentary contains a retrospective of Richard R. Ernsts life, which is filmed only a few months before his death.