We describe here two types of liquid crystalline meta-materials which exhibit large birefringence and sub-unity or negative refractive index. The conditions on the constituents' complex permittivity and permeability for producing effective refractive indices in this unconventional range are explicitly illustrated with two exemplary liquid crystalline meta-materials: (i) core-shell nano-spheres randomly dispersed in a nematic liquid crystal and (ii) planar nano-structures juxtaposed with a layer of liquid crystal. Both systems also exhibit enhanced electro-optical and nonlinear optical responses. These meta-materials may find applications in the next generation reflective, transmissive, modulation and switching elements and devices in the visible-infrared-Terahertz and microwave regimes.