Supported noble metal-comprising catalysts which can be obtained by a) application of colloidal noble metal in the form of a colloidal solution, optionally in admixture with additives acting as promoters, to a support material, b1) drying of the resulting product at from 150 to 350° C., or b2) drying of the resulting product at from 150 to 350° C. and subsequent calcination at from 350 to 550° C. for epoxidation or oxidative dehydrogenation, a process for producing it, its use and also the use of colloidal noble metal for producing supported catalysts.