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Two-and three-dimensional``random swiss-cheese percolation''and``random-site percolation''pore networks were simulated on a computer. The results were used as templates for the fabrication of model objects. The flow of water through the pore spaces of these objects was studied with the aid of NMR microscopy in the velocity-mapping variant. Up to three spatial dimensions and three dimensions for the three velocity components were examined. The results for the model objects were juxtaposed to those for lacunar materials such as pumice, sponge, sand, and glass bead agglomerates. Parameters characterizing the structure were evaluated from conventional NMR images of the water-filled pore spaces. The percolation backbone was determined by eliminating all voxels with velocities below the noise level.