This paper analyzes the accuracy of non-invasive methods to determine subject-specific kinematics of wrist axes based on unrestricted measurements. Adapting methods from the literature, joint parameters are fitted from measurements derived through an in-vivo, non-invasive procedure. This paper analyzes the accuracy of these fitting methods using a mechanical mock-up, with known geometry and kinematic structure similar to the human wrist, which provides a ground truth for assessment of accuracy. Numerical simulations show that while the range of motion affects the accuracy of parameter estimation, the relative error in the parameters is below 4% for range of motions above 20%. The method was used to fit measurements performed on a human subject and resulting parameters were applied in the design of a subject-specific, ergonomic exoskeleton, which did not significantly alter the natural motor strategies of the subject during a pointing task.