Experiments were performed to investigate the effects of amplitude and depth on the drag reduction of a NACA 0012 airfoil plunging near a free surface for a range of frequencies. Beyond the effect of the free surface, at low Strouhal numbers based on amplitude, SrA, the drag reduction follows a parabolic trend with greater effect for greater amplitude, similar to the Garrick predictions. At SrA ≈ 0.08, larger amplitudes break from this trend due to leading-edge vortex formation. As a result, smaller amplitudes become preferable for SrA > 0.12. In addition, for the first time, vortex lock-in is documented experimentally. The effect of depth is twofold; firstly with decreasing depth, there is a general departure from the Garrick trends. Secondly, a reduction in thrust is observed around a constant unsteady parameter of τ = U∞2 πf/g ≈ 0.25; around this value significant free-surface waves form that detract from thrust creation. For depths greater than two chord lengths, there is negligible free-surface effect.