We have carried out fully relativistic full-potential, spin-polarized, all-electron density-functional calculations for straight, monatomic nanowires of the 5 d transition and noble metals Os, Ir, Pt, and Au. We find that, of these metal nanowires, Os and Pt have mean-field magnetic moments for values of the bond length at equilibrium. In the case of Ir, the wire needs to be slightly stretched in order to spin polarize. An analysis of the band structures of the wires indicate that the superparamagnetic state, which our calculations suggest will affect the conductance through the wires—though not by a large amount—at least in the absence of magnetic domain walls. It should thus lead to a characteristic temperature-and field-dependent conductance, and may also cause a significant spin polarization of the transmitted current.