With a focus on weather-restricted marine operations, a comprehensive work on numerical model calibration is conducted to improve the vessel response prediction accuracy in real environmental conditions. This framework involves using existing physics-based models in which the metocean and system parameters are entered as inputs to derive vessel responses. The numerical models based on linear potential flow theory resolve only a part of the physics, i.e., it does not account for viscous damping effects. Moreover, significant uncertainties are associated with the system parameters related to the vessel operational conditions that are not known or measured directly. Therefore, the present paper integrates the vessel model with a derivative-free Lipschitz optimization technique to calibrate the vessel system parameters. For efficient optimization, the most influential variables are identified by conducting a sensitivity study for relevant quantities of interest using a cost-effective Polynomial Chaos model. The sensitivity analysis assumes independent uniform distributions for the system parameters with proper lower and upper limits. Subsequently, estimates of the highly influential variables are optimized using on-site vessel measurements, and in turn, utilized for superior response estimation. The response computations based on the numerical wave spectrum produced superior results in comparison with the results based on the parametric wave spectrum. The calibration algorithm is validated with full-scale measurements using frequency and time domain approaches for simulating vessel motions. It has been quantitatively revealed that the Center of Gravity parameters associated with the vessel operational characteristics and sea state-dependent additional damping coefficients govern the Roll response variation to a great extent. The calibration of these parameters resulted in improved Roll spectra estimations that match the measured spectra closely.