The concentration dependence of the viscosity is studied for suspensions of approximately hard, i.e., short-range repulsive, platelets. We combine rheological measurements on suspensions of sterically stabilized platelike colloids with dissipative particle dynamics simulation for disks. This yields, for the first time, results for the intrinsic viscosity of (nearly) hard plate suspensions, as well as the second- and third-order phi (platelet volume fraction) coefficients in the viscosity. The intrinsic viscosity is used to calculate the number-average aspect ratio of the platelets, which is found to be 6.5 and 12 respectively for the two suspensions studied. The measured Huggins coefficients are intermediary between the theoretical value for hard spheres and hard rods. The combined results from viscosity measurements and simulations provide insight into the effect of Peclet number, particle model, and polydispersity on the viscosity of approximately hard platelet suspensions.