The projector-augmented-wave (PAW) method of electronic calculations has the unique feature that, while it is basically a pseudopotential-like treatment of density functional theory, it keeps a connection to reconstructible all-electron wavefunctions, and thus it can be considered less an approximation, yet having generally the same computational cost when it is compared to pseudopotential methods. The zero-field splitting of spin-spin interaction energy, although it is a core instrument in the treatment of a wide range of problems involving the behavior of electron spins in various materials, has not yet been implemented in PAW. We provide here all the background considerations for implementing the calculation of the zero-field splitting tensor within the framework of PAW.