Multifidelity methods are introduced to the nondestructive evaluation (NDE) of measurement systems. In particular, Cokriging interpolation metamodels of physics-based ultrasonic testing (UT) simulation responses are utilized to accelerate the uncertainty propagation in model-assisted NDE. The proposed approach is applied to a benchmark test case of UT simulations and compared with the current state-of-the-art techniques. The results show that Cokriging captures the physics of the problem well and is able to reduce the computational burden by over one order of magnitude compared to the state of the art. To the best of the author's knowledge, this the first time multifidelity methods are applied to model-assisted NDE problems.