A method of refining a natural oil includes: (a) providing a feedstock that includes a natural oil; (b) reacting the feedstock in the presence of a metathesis catalyst to form a metathesized product that includes olefins and esters; (c) passivating residual metathesis catalyst with an agent selected from the group consisting of phosphorous acid, phosphinic acid, and a combination thereof; (d) separating the olefins in the metathesized product from the esters in the metathesized product; and (e) transesterifying the esters in the presence of an alcohol to form a transesterified product and/or hydrogenating the olefins to form a fully or partially saturated hydrogenated product. Methods for suppressing isomerization of olefin metathesis products produced in a metathesis reaction, and methods of producing fuel compositions are described.