A surface Quasi-Geostrophy based (eSQG) method to diagnose the vertical velocity field from Sea Surface Height (SSH) is assessed using high resolution simulations. These simulations concern a turbulent eddy field with large Rossby numbers and energetic wind-driven motions. Results indicate that low-frequency vertical velocities (and also horizontal motions) can be reconstructed within a range of scales between 20 km and 400 km from the surface down to 500 m. The only information needed is a single high-resolution SSH snapshot and information on the large-scale vertical stratification. Inertial motions are naturally filtered because they do not contaminate SSH as we demonstrate. These results are encouraging and further strengthen previous studies using the eSQG method. They indicate that access to high resolution SSH may represent a major advance to retrieve horizontal and vertical fluxes of any tracer in the upper ocean.