Generalized least-squares and maximum likelihood approaches for parameter estimation in multivariate response models have been prevalent in the chemical kinetics literature to date. In contrast, robust alternatives have received considerably less attention. These methods safeguard against possible deviations from the assumptions, such as the presence of outliers or non-normality of the random errors. We compare, through Monte Carlo simulation, the performance of the classical Box Draper determinant criterion (ML) to those of two robust estimators: the multivariate Huber's M-estimator and the multivariate least-trimmed squares estimator (MLTS). Although the results are not entirely conclusive, overall, we find no compelling evidence for preferring any one of the two robust methods over the conventional ML estimates. At the same time, it was unexpected to find that ML is still reasonable under mild outlier contamination and mild deviations from normality. This notwithstanding, one loses nothing by comparing ML together with MLTS to cross-check each other as a safety measure.