We report magnetic and magnetoimpedance (MI) properties of cobalt-rich amorphous alloys to investigate the role of small quantities of 3d or 4d transition-metal elements in Co-rich alloys. The microstructure, thermal stability, AC soft magnetic properties and magnetoimpedance of the ribbons are investigated by substituting Nb in place of Ni and Mn. Present study shows an improvement in glass forming ability and reduction in electrical conductivity of the ribbon with Nb substitution. Higher Nb containing alloy shows minimum core loss compared to other compositions over a range of frequencies. Ribbon with higher core loss exhibited higher MI ratio (∼100% at 3 MHz), but decreased rapidly at higher frequencies due to its larger electrical conductivity. The ribbon with lower electrical conductivity showed a steady MI ratio and field sensitivity with frequency. These results indicate that MI and core losses at medium range of frequencies can be tuned by adding Nb that provides most favourable electrical conductivity and magnetic permeability values, which result in optimum skin depth and MI. The effect of electrical conductivity on MI is also validated through numerical simulations using standard electrodynamics models. © 2017 Elsevier B.V.