In this paper, we derive the Cramér-Rao bound (CRB) for range estimation, which does not only exploit the range information in the time delay, but also in the amplitude of the received signal. This new bound is lower than the conventional CRB that only makes use of the range information in the time delay. We investigate the new bound in an additive white Gaussian noise (AWGN) channel with attenuation by employing both narrowband (NB) signals and ultra-wideband (UWB) signals. For NB signals, the new bound can be 3dB lower than the conventional CRB under certain conditions. However, there is not much difference between the new bound and the conventional CRB for UWB signals. Further, shadowing effects are added into the data model. Several CRB-like bounds for range estimation are derived to take these shadowing effects into account.