Results from stochastic reconstruction of porous solids and from a direct comparison of calculated and experimental effective transport properties are presented. Eight porous solids of different microstructures were selected to evaluate the performance of two reconstruction methods based on simulated annealing. The common method was constrained by the two-point probability function and the lineal-path function for the void phase, whilst the constraints of our new method were further supplemented by the lineal-path function for the solid phase and by two adjustable parameters. The new method was capable of reproducing the void and solid phases as large clusters spanning the entire replicas. Non-percolating clusters formed minor volume fractions of both phases. Although the common method reproduced the microstructures quite well, their pore space connectivity was significantly poorer. Therefore, effective permeability, effective ordinary diffusivity, and effective Knudsen diffusivity calculated for the replicas obtained using the new method were always much greater than the same quantities related to the common reconstruction method. For most of the porous solids, values of the effective properties calculated on the basis of the new reconstruction method better matched their experimental counterparts than the corresponding values derived from the microstructures reproduced using the common reconstruction method.