Calibration of the rock-frame elastic properties is an important step in establishing the rock-physics models for quantitative seismic reservoir characterization. While several empirical and theoretical rock-frame models have been proposed in the literature, their applicability to carbonate rocks is challenged due to their specific textural and varied pore type characteristics. Here, the suitability of an empirical model (Nur's critical porosity), and a semi-empirical inclusion-based model (Keys-Xu) for a hard rock carbonate reservoir in south-west Iran is examined. Wireline log data in conjunction with deterministic and probabilistic optimization algorithms are employed to calibrate the free parameters in these models, as well as the minerals' effective elastic moduli and density. The optimum values derived from the very fast simulated annealing algorithm were comparable to the estimated values from a probabilistic calibration workflow (Markov chain Monte Carlo sampling-based method). The uncertainty quantification via the probabilistic approach indicates higher uncertainty is associated with the calibrated clay elastic parameters (10%-13%) compared to the uncertainty associated with the calcite elastic moduli (1%-3%) in both rock-frame models. This could be attributed to the dominance of the calcite mineral and lack of variability in clay volume fraction in the interval of interest. The uncertainty associated with critical porosity and pore aspect ratio are 3% and 7%, respectively. The results of this case study show that simple rock frame models with only one free parameter (critical porosity or pore aspect ratio) could successfully model the elastic logs without resorting to more sophisticated rock-frame models.