Existing bias mitigation methods to reduce disparities in model outcomes across cohorts have focused on data augmentation, debiasing model embeddings, or adding fairness-based optimization objectives during training. Separately, certified word substitution robustness methods have been developed to decrease the impact of spurious features and synonym substitutions on model predictions. While their end goals are different, they both aim to encourage models to make the same prediction for certain changes in the input. In this paper, we investigate the utility of certified word substitution robustness methods to improve equality of odds and equality of opportunity on multiple text classification tasks. We observe that certified robustness methods improve fairness, and using both robustness and bias mitigation methods in training results in an improvement in both fronts