Physical symmetries provide a strong inductive bias for constructing functions to analyze data. In particular, this bias may improve robustness, data efficiency, and interpretability of machine learning models. However, building machine learning models that explicitly respect symmetries can be difficult due to the dedicated components required. Moreover, real-world experiments may not exactly respect fundamental symmetries at the level of finite granularities and energy thresholds. In this work, we explore an alternative approach to create symmetry-aware machine learning models. We introduce soft constraints that allow the model to decide the importance of added symmetries during the learning process instead of enforcing exact symmetries. We investigate two complementary approaches, one that penalizes the model based on specific transformations of the inputs and one inspired by group theory and infinitesimal transformations of the inputs. Using top quark jet tagging and Lorentz equivariance as examples, we observe that the addition of the soft constraints leads to more robust performance while requiring negligible changes to current state-of-the-art models.