Two-component particle image velocimetry and surface pressure measurements are used to characterize the flow field over a plunging nominally two-dimensional at-plate airfoil at zero geometric angle of attack, and a finite wing with rectangular planform and a semi- aspect-ratio sAR = 2. Phase-averaged horizontal and vertical planes of PIV data are used to reconstruct a three-dimensional volume in which the evolution of the vortex structure is rendered, and vorticity transport is quantified within a chordwise planar control volume bounded by the at plate surface, and containing the leading-edge vortex. It is shown that, for the two-dimensional airfoil, generation of secondary vorticity of opposite sign to the leading-edge vortex occurs at a rate of approximately half that of the leading-edge shear layer flux, suggesting that entrainment of this vorticity into the leading-edge vortex has a significant impact on the strength of the vortex. Also, spanwise convection of vorticity has a non-negligible impact on control-volume circulation during the second half of the stroke. In the case of the finite wing, the initial development of the leading-edge vortex is qualitatively similar to that of the nominally two-dimensional case; however, through the mid-portion of the stroke, the leading-edge vortex rapidly evolves into an arch structure as it convects along the chord, as seen in previous studies. In contrast to the case of the nominally two-dimensional airfoil, spanwise flow acts to significantly deplete the circulation within the leading-edge vortex. The difference between control-volume circulation and the sum of the integrated convective boundary fluxes suggests that the fraction of the total vorticity flux supplied by the finite wing surface beneath the leading-edge vortex is similar to that of the two-dimensional case.