Nonlinear hydrodynamic effects influence the power capture of resonant wave energy converters (WECs), particularly within the frequency band where these devices are designed to operate. In this study, wave flume experiments are conducted on a semi-immersed spherical model with prescribed heave motions, emulating the response to an incident broad-banded wave group. Several body motion amplitudes (up to a maximum displacement of greater than half the radius) are tested at different peak frequencies, revealing progressive reductions in both the first-harmonic radiation forces and radiated wave elevations, per unit motion amplitude, as the motion amplitude is increased. A simple partially nonlinear potential flow model incorporating instantaneous ‘volume flow’ corrections shows very good agreement with the measured radiated waves, capturing the dominant nonlinear trends. An experimental decomposition of the radiated field into channel modes is also performed, based on linear theory while accounting for linear viscous dissipation. This is then used to calculate the power in the radiated field compared to the input power from the moving body over a frequency band of interest. The model and experiments show a consistent, monotonic decrease in normalised radiated power as the amplitude of body motion increases. Overall, the findings indicate that linear theory is remarkably accurate even for quite large body motions. The most important nonlinear corrections in the first-harmonic frequency range arise from third-order potential flow interactions, fundamentally caused by the spherical geometry, and demonstrate the potential utility of volume flow models for assessing WEC radiation.