Ridge waveguides provide a large refractive index contrast and thus strong mode confinement, making them highly attractive for building compact photonic integrated circuits. However, ridge waveguides suffer from scattering losses. We demonstrate scattering-loss reduction of ridge waveguides made of lithium-niobate-on-insulator (LNOI) substrates by more than one order of magnitude. This is achieved by gently polishing of the ridge's sidewalls and simultaneous protection of the top surfaces by a metal layer. Whispering-gallery-resonator loss measurements reveal ultra-low losses down to 0.04 dB/cm of the processed waveguides. Our approach pushes ridge waveguides further towards their fundamental absorption-loss limit, enabling highly efficient integrated devices.