This work reports measurements with a concave lens based on a photonic crystal (PC) structure, which was designed to have an effective index of refraction n _eff < 1 or even < 0, and which is intended as a model system for future down-scaled optical elements based on PCs with an unusual effective index. The dimensions of the model PC were optimized for experiments in the microwave regime around 10 GHz. Calculations for a material with no losses allowed to select the wave-lengths for which the lens could be expected to behave as a homogeneous meta-material with an unusual effective refractive index. The field distribution behind the lens was measured, and good focusing efficiencies for n _eff < 1 were found for perfect and strongly disturbed PC's in reasonable accordance with the predictions. The (down-scaled) model system investigated thus can serve as a reference for testing PC-based optical elements made from materials which so far elude reliable predictions, e.g. doped semiconductors, nano-rod assemblies, or meta-materials with anisotropic behavior.