In a joint experimental and theoretical study, we investigate the bias-voltage dependence of the tunnel magnetoresistance (TMR) through a vacuum barrier. The TMR observed by spin-polarized scanning tunneling microscopy between an amorphous magnetic tip and a Co(0001) sample is almost independent of the bias voltage at large tip-sample separations. Whereas qualitative understanding is achieved by means of the electronic surface structure of Co, the experimental findings are compared quantitatively with bias-voltage dependent first-principles calculations for ballistic tunneling. At small tip-sample separations, a pronounced minimum in the experimental TMR was found at +200 mV bias.