In a case study of the waveform design for target estimation in MIMO sensing,  developed the optimum wave-form design in the presence of colored noise, as well as the joint robust transmitter and receiver designs. Three criteria, namely mutual information (MI), minimum mean square error (MMSE), and normalized MSE (NMSE), are considered. The relationship between the essential measure MI in communications and the commonly adopted MSE indicators for sensing has created a vision of communications-inspired sensing. In this paper, we will further investigate this relationship by analyzing the sensitivity of the optimum design to the overestimation error. For each of the three criteria, we derive the explicit formula for the error mode strength threshold, above which the error mode would consume nonzero transmit power and the original waveform design will be inevitably altered. We also develop a normalized NMSE indicator to measure the estimation performance variation induced by the error mode. Both analytical and numerical results confirm that the optimum waveform designs based on the three criteria do not show significant performance deterioration. While the NMSE-based optimum solution is always more sensitive to the overestimation error than the MI-based one, there is no universal relationship between these two criteria and MMSE.