Terahertz (THz) electric field pulses containing frequency components across an ultra-wide spectrum are important for spectroscopy investigations, and are valuable to improving the application of THz radiation to the security, medical, and communication industries. We perform 2D finite-difference time-domain simulations of sub-wavelength LiNbO3 (LN) waveguides (i.e. waveguides having core dimensions that are sub-wavelength with respect to the femtosecond optical pump pulse). The sub-wavelength aspect of these waveguiding structures maximizes the intensity of the pump pulse in the LN core, while also minimizing the LN reststrahlen band absorption. Notably, Cherenkov radiation is generated at frequencies between 0.18 and 106 THz, where the sub-wavelength nature of the waveguides allows for Cherenkov emission at ~47° over the entire frequency spectrum. Additionally, we show how a 100 μm×1 mm×500 nm waveguide (pumped by a 780 nm, 7 fs, 1 nJ femtosecond pulse) produces a 140 fJ THz electric field pulse.