Bayesian optimization (BO) is an efficient framework for optimization of black-box objectives when function evaluations are costly and gradient information is not easily accessible. BO has been successfully applied to automate the task of hyperparameter optimization (HPO) in machine learning (ML) models with the primary objective of optimizing predictive performance on held-out data. In recent years, however, with ever-growing model sizes, the energy cost associated with model training has become an important factor for ML applications. Here we evaluate Constrained Bayesian Optimization (CBO) with the primary objective of minimizing energy consumption and subject to the constraint that the generalization performance is above some threshold. We evaluate our approach on regression and classification tasks and demonstrate that CBO achieves lower energy consumption without compromising the predictive performance of ML models.