The constrained Cramer-Rao bound (CRB) has been used successfully to study parameter estimation in flat-fading scenarios, and established the value of side information such as known waveform properties (e.g. constant modulus) and known training symbols. There are classes of communication links, however, that may be subject to highly dynamic changes, and this could cause the assumed data model to be an inaccurate model of the channel. Therefore, the constrained misspecified CRB is considered to explore the impact of model mismatch for such communication links. Specifically, quantifying the loss in estimation performance when one assumes the channel is stationary when it is not is of interest.