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First-principles calculations have been carried out to reveal structural, electromechanical, electronic, and lattice dynamical properties of $\mathrm{GaN}∕\mathrm{ScN}$ and $\mathrm{InN}∕\mathrm{ScN}$ superlattices\char22{}made by alternating hexagonal layers of GaN, or InN, with hexagonal layers of ScN\char22{}for different periods and overall compositions. These nitride systems belong to two different structural classes (having different coordination number), depending on the overall composition. For Sc compositions larger than 50%, each atom has nearly five nearest neighbors. On the other hand, Sc-deficient superlattices adopt a ground state that is nearly fourfold coordinated. This change of structure, and the change in composition or period within the same structure, considerably affect the piezoelectric response, the electronic band gap in magnitude as well as in character (indirect versus direct), and the phonon spectra. We also discussed the relevance of some of these predictions for designing future technological applications.