Much recent attention has been paid to wavefront sensing by phase-diverse phase retrieval (PDPR): estimating the wavefront in an exit pupil based on point-spread function measurements that incorporate known additional aberrations. The Next-Generation Space Telescope (NGST), for example, is expected to rely on this technology. This paper studies narrowband PDPR via "point-by-point" reconstruction, which estimates the phase at each sampled point in the pupil plane without using basis functions. The performance of an iterative, point-by-point phase diversity (PD) algorithm is demonstrated on data from an NGST-oriented wavefront sensing and control testbed as well as simulated data. Encouraging performance is exhibited in simulation and on experimental images in the presence of mild, continuous aberrations; however, in the presence of larger, discontinuous aberrations the experimental performance is poorer. The estimation algorithm is also used to compute Cramer-Rao bounds (CRBs) for a simulated PDPR problem and to analyze their sensitivity to system parameters such as field-of-view, wavelength, and the amount of focus diversity.