X-ray microtomography can provide valuable three-dimensional images of the microstructure of porous building materials, but the chosen resolution of the images must be carefully selected to balance pore size and representative elementary volume concerns. Too high a resolution provides excellent individual pore delineation, but results in an overall volume which is too small to be representative. Too low a resolution provides a good representative elementary volume, but may result in pores which are difficult to isolate and whose 3-D connectivity is less than the pores in the actual material. For a material with a wide range of pore sizes (such as cement paste or mortar), it will be extremely difficult to balance these two concerns and a multi-scale approach, such as that used for computing the diffusivity of the lime silica brick in this study, may be needed to produce quantitative comparisons to experimental data. When these concerns are properly balanced, or at least considered in the subsequent computations of transport properties, the computed transfer coefficients compare favorably with their experimental counterparts. Experimentally, if it is suspected that a material may be anisotropic, transfer coefficients should be measured in each of the three principal directions to test this hypothesis. Finally, it has been demonstrated that the Katz-Thompson relationship can be used to characterize the transport properties and pore sizes of the bricks examined in this study.