Reversible, diffusionless, first-order solid-solid phase transitions accompanied by caloric effects are critical for applications in the solid-state cooling and heat-pumping devices. Accelerated discovery of caloric materials requires reliable but faster estimators for predictions and high-throughput screening of system-specific dominant caloric contributions. We assess reliability of the computational methods that provide thermodynamic properties in relevant solid phases at or near a phase transition. We test the methods using the well-studied B2 FeRh alloy as a “fruit fly” in such a materials genome discovery, as it exhibits a metamagnetic transition which generates multicaloric (magneto-, elasto-, and baro-caloric) responses. For lattice entropy contributions, we find that the commonly-used linear-response and small-displacement phonon methods are invalid near instabilities that arise from the anharmonicity of atomic potentials, and we offer a more reliable and precise method for calculating lattice entropy at a fixed temperature. Then, we apply a set of reliable methods and estimators to the metamagnetic transition in FeRh (predicted 346 ± 12 K, observed 353 ±1 K) and calculate the associated caloric properties, such as isothermal entropy and isentropic temperature changes.