  A high-precision relativistic calculations of Cd-like Nd$^{12+}$, Sm$^{14+}$
and Sn-like Pr$^{9+}$, Nd$^{10+}$ atomic properties is carried out using an
approach that combines configuration interaction and a linearized
coupled-cluster method. These ions have long-lived metastable states with
transitions accessible by laser excitations, relatively simple electronic
structure, high sensitivity to $\alpha$ variation, and stable isotopes. Breit
and QED corrections were included into the calculations. Energies, transition
wavelengths, electric- and magnetic-multipole reduced matrix elements,
lifetimes, and sensitivity coefficients $q$ and $K$ to the variation of the
fine-structure constant $\alpha$ were obtained. A detailed study of
uncertainties was performed. Energies for similar Cd-like Ba$^{8+}$, La$^{9+}$,
Ce$^{10+}$, Pr$^{11+}$ and Sn-like Ba$^{6+}$ ions were calculated and compared
with experiment for further tests of the accuracy.
