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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 anapproach that combines configuration interaction and a linearizedcoupled-cluster method. These ions have long-lived metastable states withtransitions accessible by laser excitations, relatively simple electronicstructure, high sensitivity to $\alpha$ variation, and stable isotopes. Breitand QED corrections were included into the calculations. Energies, transitionwavelengths, electric- and magnetic-multipole reduced matrix elements,lifetimes, and sensitivity coefficients $q$ and $K$ to the variation of thefine-structure constant $\alpha$ were obtained. A detailed study ofuncertainties was performed. Energies for similar Cd-like Ba$^{8+}$, La$^{9+}$,Ce$^{10+}$, Pr$^{11+}$ and Sn-like Ba$^{6+}$ ions were calculated and comparedwith experiment for further tests of the accuracy.

Atomic properties of Cd-like and Sn-like ions for the development of frequency standards and search for the variation of the fine-structure constant