We investigated the applicability of two non-Newtonian constitutive models (Casson and Herschel-Bulkley models) in the determination of the blood viscosity and yield stress using a pressure-scanning microfluidic hemorheometer. The present results were compared with the measurements through a precision rheometer (ARES2). For a Newtonian fluid (standard oil), the two constitutive models showed excellent agreement with a reference value and the measurement of ARES2. For human blood as a non-Newtonian fluid, both the Casson and Herschel-Bulkley models exhibited similar viscosity results over a range of shear rates and showed excellent agreement with the ARES2 results. The Herschel-Bulkley model yielded a slightly higher value than other results at low shear rates (${gamma}<10$), which may be due to the relatively high value of the yield stress. The yield stress values for whole blood were 14.4 mPa for the Casson model and 32.5 mPa for the Herschel-Bulkley model, respectively. Thus, the present study showed that the Casson model would be better than the Herschel-Bulkley model for representing the non-Newtonian characteristics of blood viscosity.