A higher order finite-difference time-domain perfectly matched layer (PML) methodology for the systematic modeling of generalized three-dimensional electromagnetic compatibility (EMC) problems, is presented in this paper. Establishing a covariant/contravariant formulation, the novel algorithm introduces a parametric topology of accurate nonstandard schemes for the nonorthogonal div-curl problem and the suppression of lattice dispersion. Also, the wider boundary stencils are treated by compact operators, while a mesh expanding process reduces the absorber's depth. At arbitrarily-aligned interfaces, consistency is preserved through a convergent concept that considers the proper continuity conditions. Hence, the enhanced PMLs attain large annihilation rates for complex domains and broadband spectrums. Numerical validation-stressing on evanescent waves near scatterers-confirms the superiority of the proposed algorithm via realistic EMC applications, like shielding enclosures, printed circuit boards, and modern antennas.