We present an effective approach to calculating the low-frequency part of the spectrum of uniaxially patterned periodic structures. In this approach we ignore to zeroth-order the Bragg scattering by crystalline planes but include local field effects in first order perturbation theory. Bragg reflections are shown to be important only near points of symmetry-induced spectral degeneracy, where they can be taken into account by the degenerate perturbation theory. We apply this approach to waveguiding by thin patterned slabs embedded in a homogeneous medium. This results in an effective medium approximation, similar to the Maxwell Garnet theory but modified for the local field corrections specific to 2D geometry. Slab spectra are well described by a single frequency-independent parameter, which we call the guiding power. Simple analytic formulae are presented for both TM and TE polarizations. Comparing these formulae with similar expressions for homogeneous uniaxial slabs of same thickness, we derive the principal values of the effective homogeneous permittivity that provides identical waveguiding. We also discuss the extinction of waves due to the Rayleigh-like scattering on lattice imperfections in the slab. The TE waves that are normally better confined are scattered out more effciently, in part because of the higher scattering cross-section and in part because the better confinement leads to higher exposure of TE waves to lattice imperfections in the slab.