Near-surface voids and pores are generated in metal processing operations as diverse as additive manufacturing and powder processing, but their effect on indentation hardness has not been explored outside homogenized frameworks. Here we model the micromechanics of near-surface void deformation up to closure in a wedge-indentation field in ductile metal, and reveal the considerable softening effect of voids on the indentation hardness. Both symmetrically and eccentrically located voids, at various depths below the free surface, are studied. Notably, the extent of apparent reduction in the elastic modulus due to a void is much smaller than its effect on apparent hardness, e.g. 6.5% against 55% for the same void. Critical to the simulations is an adaptive remeshing finite element (FE) framework that allows accurate capture of processes like void closure and void-wall self-contact. The simulations reveal the subsurface plastic strain, strain-rate, and velocity fields with high fidelity, and their radical differences from the radial indentation field in a void-free specimen. These differences include the presence of localized pockets of high and low strain, and the initial accommodation of material displaced by the indenter by a corresponding reduction in void area. Unlike voids under uniform compression, the void-area evolution in indentation shows a characteristic sigmoidal pattern of reduction with indentation depth for all but the smallest voids. Interestingly, the indented surface profile can exhibit a one-sided pile-up feature which is diagnostic of the presence of an eccentrically located sub-surface void. Our remeshing scheme is versatile, as exemplified by its ability to model the extreme deformation associated with two nearly closed-spaced voids under an indenter. Our work shows that void-closure simulations in related applications like forming could benefit from the adoption of a remeshing framework.