Structures and magnetic properties of gold-coated transition-metal clusters [Mn-13@Au-20](-) and [Co-13@Au-20](-) are studied within the framework of gradient-corrected density functional theory. The gold coating can result in either an enhanced or an attenuated effect on the magnetism of the core clusters. For [Mn-13@Au-20](-), the total magnetic moment is greatly enhanced to as high as 44 mu(B), more than 20-fold higher than that of the bare Mn-13(-) cluster. For [Co-13@Au-20](-), however, the gold coating gives rise to an attenuation effect which leads to a reduction of the magnetic moment to 20 mu(B) from 30 mu(B) of the bare Co-13(-) cluster.