We use coupled mode theory, adequately incorporating optical losses, to model ultra-broadband terahertz (THz) waveguide emitters (0.1-20 THz) based on difference frequency generation of femtosecond infrared (IR) optical pulses. We apply the model to a generic, symmetric, five-layer, metal/cladding/core waveguide structure using transfer matrix theory. We provide a design strategy for an efficient ultra-broadband THz emitter and apply it to polymer waveguides with a nonlinear core composed of a poled guest-host electro-optic polymer composite and pumped by a pulsed fiber laser system operating at 1567 nm. The predicted bandwidths are greater than 15 THz and we find a high conversion efficiency of 1.2 × 10(-4) W(-1) by balancing both the modal phase-matching and effective mode attenuation.