This study developed a Calvet calorimeter-based measurement system for determining the mass-specific isobaric specific heat capacity ( \({c}_{p}\) in J·g⁻1·K⁻1) of the ultra-low-GWP refrigerant R1132a (1,1-difluoroethene) and its binary mixtures with R13I1 (trifluoroiodomethane). The system was upgraded from prior configurations for pure refrigerants to accommodate precise mixture preparation, incorporating custom control software for synchronized operation and enhanced safety features for high-pressure experiments. Specific heat capacities were measured via the two-step method under controlled temperature (203.15–333.15 K) and pressure (up to 100 bar) conditions, with detailed attention to baseline stability, stem temperature control, and pressure fluctuations. All measurements were conducted in the compressed liquid phase at pressures at least 5 bar above the saturation pressure. Experimental results are reported for pure R1132a and three mixture compositions (R1132a/R13I1 molar ratios of 75:25, 50:50, and 25:75). A comprehensive uncertainty analysis conducted in accordance with the GUM framework resulted in expanded uncertainties (coverage factor \(k\) =2) ranging from 4.5 % to 5.9 % depending on composition, with the primary contributions arising from the integration of heat quantity, density estimation, and measurements of temperature and pressure. These measurements provide essential thermodynamic data for developing equations of state for next-generation low-GWP refrigerant blends suitable for ultra-low-temperature refrigeration cycles.