Third-harmonic generation (THG) in silicon nitride waveguides is an ideal source of coherent visible light, suited for ultrafast pulse characterization, telecom signal monitoring and self-referenced comb generation due to its relatively large nonlinear susceptibility and CMOS compatibility. We demonstrate third-harmonic generation in silicon nitride waveguides where a fundamental transverse mode at 1,596 nm is phase-matched to a TM02 mode at 532 nm, confirmed by the far-field image. We experimentally measure the waveguide width-dependent phase-matched wavelength with a peak-power-normalized conversion efficiency of 5.78 × 10−7 %/W2 over a 660-μm-long interaction length.