A new approach to reduce the bending loss of the fundamental quasi-transverse magnetic mode in optical waveguides is presented. A much lower bending loss is achieved by designing waveguides that use as substrate or cladding an anisotropic metamaterial made of multilayers of thin films of germanium and porous silica instead of a conventional silica substrate or cladding. We numerically demonstrate a reduction in the bending loss of up to ∼3 dB/90° for a silicon-on-insulator (SOI) waveguide of the standard core size (500 × 220 nm), as well as, up to ∼ 10 dB/90° for a sub-wavelength SOI waveguide of core size (372 × 186 nm), even considering the high absorption of the germanium layers in the cladding, both designed to operate at 1550 nm.