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To correlate the mechanical properties of granular porous materials with their microstructure, typically porosity is being considered as the dominant parameter. In this work, we suggest the average coordination number, i.e., the average number of connections that each grain of the porous material has to its neighboring grains, as additional — and possibly even more fundamental — microstructural parameter. In this work, a combination of stochastic and mechanical modeling is applied to study microstructural influences on the elastic properties of porous ceramics. This is accomplished by generating quasi-two-dimensional (2D) and fully three-dimensional (3D) representative volume elements (RVEs) with tailored microstructural features by a parametric stochastic microstructure model. In the next step, the elastic properties of the RVEs are characterized by finite element analysis. The results reveal that the average coordination number exhibits a very strong correlation with the Young’s modulus of the material in both 2D and 3D RVEs. Moreover, it is seen that quasi-2D RVEs with the same average coordination number, but largely different porosities, only differ very slightly in their elastic properties such that the correlation is almost unique. This finding is substantiated and discussed in terms of the load distribution in microstructures with different porosities and average coordination numbers