Dispersion properties of electromagnetic crystals formed by small uniaxial resonant scatterers (magnetic or electric) are studied using the local field approach. The goal of the study is to determine the conditions under which the homogenization of such crystals can be made. Therefore the consideration is limited by the frequency region where the wavelength in the host medium is larger than the lattice periods. It is demonstrated that together with known restriction for the homogenization related with the large values of the material parameters there is an additional restriction related with their small absolute values. From the other hand, the homogenization becomes allowed in both cases of large and small material parameters for special directions of propagation. Two unusual effects inherent to the crystals under consideration are revealed: flat isofrequency contour which allows subwavelength imaging using canalization regime and birefringence of extraordinary modes which can be used for beam splitting.