A high-precision relativistic calculation of Cd-like Nd12+, Sm14+ and Sn-like Pr9+, Nd10+ 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 Ba8+, La9+, Ce10+, Pr11+ and Sn-like Ba6+ ions were calculated and compared with experiment for further tests of the accuracy.