Supported by the wide range of available medical data available, cardiac biomechanical modeling has exhibited significant potential to improve our understanding of heart function and to assisting in patient diagnosis and treatment. A critical step towards the development of accurate patient-specific models is the deployment of boundary conditions capable of integrating data into the model to enhance model fidelity. This step is often hindered by sparse or noisy data that, if applied directly, can introduce non-physiological forces and artifacts into the model. To address these issues, in this paper we propose novel boundary conditions which aim to balance the accurate use of data with physiological boundary forces and model outcomes through the use of data-derived boundary energies. The introduced techniques employ Lagrange multipliers, penalty methods and moment-based constraints to achieve robustness to data of varying quality and quantity. The proposed methods are compared with commonly used boundary conditions over an idealized left ventricle as well as over in vivo models, exhibiting significant improvement in model accuracy. The boundary conditions are also employed in in vivo full-cycle models of healthy and diseased hearts, demonstrating the ability of the proposed approaches to reproduce data-derived deformation and physiological boundary forces over a varied range of cardiac function.