Model independent constraints on the mass of extra neutral gauge bosons and their couplings to charged leptons are given for LEP~II and a 500\,GeV $e^+e^-$ collider. Analytical exclusion limits are derived in the Born approximation. The $Z'$ limits obtained with radiative corrections are always worse than those calculated at the Born level. Polarized beams are only useful for degrees of polarization essentially larger than 50\%. Known discovery limits on extra $Z$ bosons predicted by popular $Z'$ models are reproduced as special cases. The $Z'$ constraints are compared to those predicted by four fermion contact interactions.