High-grade knee laxity is associated with early anterior cruciate ligament (ACL) graft failure, poor function, and compromised clinical outcome. Yet, the specific ligaments and ligament properties driving knee laxity remain poorly understood. We described a Bayesian calibration methodology for predicting unknown ligament properties in a computational knee model. Then, we applied the method to predict unknown ligament properties with uncertainty bounds using tibiofemoral kinematics and ACL force measurements from two cadaver knees that spanned a range of laxities; these knees were tested using a robotic manipulator. The unknown ligament properties were from the Bayesian set of plausible ligament properties, as specified by their posterior distribution. Finally, we developed a calibrated predictor of tibiofemoral kinematics and ACL force with their own uncertainty bounds. The calibrated predictor was developed by first collecting the posterior draws of the kinematics and ACL force that are induced by the posterior draws of the ligament properties and model parameters. We took the median value of the draws as the predicted value and the 5% and 95% quantiles of the draws for the uncertainty bounds. Bayesian calibration identified unique ligament slack lengths for the two knee models and produced ACL force and kinematic predictions that were closer to the corresponding in vitro measurement than those from a standard optimization technique. This Bayesian framework quantifies uncertainty in both model parameters and ligament properties; an important step towards developing subject-specific computational models for improving treatment of ACL injury.