We investigate the calibration of the uncertainties of thermal scattering of ZrHx in the fuel material in TRIGA reactor simulations. Thermal scattering cross sections of ZrHx are heavily affected by the solid-state frequency distributions, also called phonon spectra. In previous work, we proposed parameterized phonon spectrum models and explored the effects on quantities of interest (QoIs) of changing spectra with such models by varying the parameters. In this work, we establish a more general calibration framework for the phonon spectrum of ZrHx. To accomplish this calibration, we introduce two emulators, Gaussian process regression and Bayesian multivariate adaptive regression splines, to create a map from the input parameters to the QoIs into the calibration framework. Using these emulators, we perform calibrations using the emulation results with the same QoIs at 600 K. Test simulations using data generated with calibrated parameters show that uncertainties of the QoIs shrink over 50%. Moreover, we extend the test to the reactivity at a different temperature, 293.6 K, as an extrapolated test of the calibration, and obtained results close to those of the surrogate experiment. The efficacy and efficiency of implementing emulators in the calibration framework are demonstrated.