Energy dissipation rates during ocean wave breaking are estimated from high-resolution profiles of turbulent velocities collected within 1 m of the surface.The velocity profiles are obtained from a pulse-coherent acoustic Doppler sonar on a wave-following platform, termed a Surface Wave Instrument Float with Tracking, or "SWIFT", and the dissipation rates are estimated from the structure function of the velocity profiles. The purpose of the SWIFT is to maintain a constant range to the time-varying surface and thereby observe the turbulence in breaking crests (i.e., above the mean still water level). The Lagrangian quality is also useful to pre-filter wave orbital motions and mean currents from the velocity measurements, which are limited in magnitude by phase-wrapping in the coherent Doppler processing. Field testing and examples from both offshore whitecaps and nearshore surf breaking are presented. Dissipation is elevated (up to 10-3 m2 s-3) during strong breaking conditions, which are confirmed using surface videos recorded onboard the SWIFT. Although some velocity contamination is present from platform tilting and heaving, the structure of the velocity profiles is dominated by a turbulent cascade of eddies (i.e., the inertial sub-range). The noise, or uncertainty, in the dissipation estimates is shown to be normally distributed and uncorrelated with platform motion. Aggregated SWIFT measurements are shown to be useful in mapping wave breaking dissipation in space and time.