We investigate dynamic effective anisotropy in photonic crystals (PCs) through a combination of an effective medium theory, which is a high-frequency homogenization (HFH) method explicitly developed to operate for short waves, as well as through numerical simulations and microwave experiments. The HFH yields accurate predictions of the effective anisotropic properties of periodic structures when the wavelength is of comparable order to the pitch of the array; specifically, we investigate a square array of pitch 2 cm consisting of dielectric rods of radius 0.5 cm and refractive index n=6√ within an air matrix. This behaves as an effective medium, with strong artificial anisotropy, at a frequency corresponding to a flat band emerging from a Dirac-like point in transverse magnetic (TM) polarization. At this frequency, highly directive emission is predicted for an electric source placed inside this PC, and this artificial anisotropy can be shown to coincide with a change of character of the underlying effective equation from isotropic to unidirective, with coefficients of markedly different magnitudes appearing in the effective equation tensor. In transverse electric (TE) polarization, we note a second radical change of character of the underlying effective equation, this time from elliptic to hyperbolic, near a frequency at which a saddle point occurs in the corresponding dispersion curves. Delicate microwave experiments are performed in both polarizations for such a PC consisting of 80 rods, and we demonstrate that a directive emission in the form of a + (respectively, an X) is indeed seen experimentally at the predicted frequency 9.5 GHz in TM polarization (respectively, 5.9 GHz in TE polarization). These are clearly dynamic effects since in the quasistatic regime the PC just behaves as an isotropic medium.