In this study, we carried out the Vickers microhardness for Cu0.5Tl0.5Ba2Ca2Cu3O10−δ, (Cu0.5Tl0.5)-1223 superconducting phase added with BaSnO3 nanoparticles. BaSnO3 nanoparticles were prepared by the co-precipitation technique, while the superconductor samples of type (BaSnO3)xCu0.5Tl0.5Ba2Ca2Cu3O10−δ, with 0.00 ≤ x ≤ 1.00 wt.%, were prepared by the conventional solid-state reaction method. Vickers microhardness (Hv) was measured at room temperature and was computed by taking the average of three hits at different locations on the specimen surface. The measurements were performed as a function of the applied load (F = 0.98–9.80 N) and the dwell time (t = 10–59 s). The Hv values were found to be strongly dependent on both the BaSnO3 content and the dwell time. Furthermore, the load independent Vickers microhardness was analyzed using Meyer’s law and different models such as the Hays–Kendall approach (HK), the elastic/plastic deformation model (EPD), the proportional specimen resistance model (PSR) and the modified proportional specimen resistance model (MPSR). The PSR model is found to be the most adequate model in explaining the load independent microhardness for the (BaSnO3)x/(Cu0.5Tl0.5)-1223 superconductor phase. Some important mechanical parameters such as Young’s modulus (E), yield strength (Y), fracture toughness (K) and brittleness index (B) were calculated as a function of x. It was found that the addition of proper concentrations of BaSnO3 nanoparticles enhanced the mechanical properties of the prepared samples. The time-dependent microhardness was investigated according to indentation creep experiments showing that the operative creep mechanisms in the studied samples were diffusion creeps at low loads followed by grain boundary sliding as well as dislocation creeps for higher loads.