Thus far, the vector field of light probed by a nanostructured super-oscillatory lens (SOL) has mostly been studied by approximate theoretical means. Here the first rigorous electromagnetic (EM) test has been presented through an established electromagnetic model solved by the three-dimensional (3D) finite-difference time-domain (FDTD) method. It is found through comparisons that scalar/vectorial theories currently used for designing the metal-film-coated SOL can effectively predict the on-axis intensity behind a SOL simulated by FDTD for both linearly and circularly polarized beams; however, they cannot reflect the true 3D EM vector field distribution particularly for the linearly polarized beam and imprecise results for the total electric energy density have appeared in certain transverse planes, e.g. a relative error as high as 26% is produced for the size of the main focus behind a SOL of 14 μm large in diameter. Besides, it is found that current theories cannot be used for designing the glass-etched phase-type SOL.