A process for removing ruthenium or ruthenium-containing compounds from a reaction mixture comprising a compound of the following formula I in an organic solvent using supercritical fluid processing techniques: wherein RA, R3, R4, D and A are as defined herein. This invention has particular application for removing ruthenium-containing catalyst and ruthenium-containing catalyst by products from reaction mixtures that result from ring-closing olefin metathesis (RCM) reactions.