The generation of coherent, ultra-broadband terahertz (THz) radiation pulses spanning more than a few octaves is vital to understanding the ultrafast response of elementary excitations, molecules, nanostructures, materials, and explore device functionality across a wide spectrum. In this work, we use 2D finite-difference time-domain simulations to show that ultra-broadband (0.18-106 THz) Cherenkov radiation can be produced from SiO2:MgO-LiNbO3:SiO2 waveguides having core dimensions that are sub-wavelength with respect to the optical pump pulse being guided. These sub-wavelength core dimensions allow the ultra-broad Cherenkov radiation to be emitted at an angle between 47.2 degrees and 47.5 degrees (dictated by the Si cladding layer dispersion), making these waveguide structures superior to the THz generation arrangements in bulk MgO-LiNbO3 crystals. When excited by a 7 fs, 780 nm laser pulse having an energy of 2 nJ, a 300 mu m-long waveguide with transverse core dimensions of 500 nm x 2 mm can generate a sub-ps, kV/ cm electric field pulse. Unlike THz pulse generation in bulk MgO-LiNbO3 crystals, having sub-wavelength core dimensions reduce the absorption from the MgO-LiNbO3 reststrahlen bands. These sub-wavelength SiO2:MgO-LiNbO3:SiO2 waveguides are ideal for on-chip applications that require ultra-broadband, compact THz sources. (C) 2017 Optical Society of America