Effect of doping in Na_0.5Bi_0.5Ti$_{O3}$ (NBT) with Ce³⁺ and Sm³⁺ at the A-site on dielectric behaviour, impedance and conductivity is being reported. Na_0.5Bi$_{0.5−x}𝐴_{x}$TiO₃ samples (A being Ce and Sm) are studied with varying values of 𝑥. For Na_0.5Bi$_{0.5−x}$Ce$_{x}$TiO₃ samples 𝑥 is 0.001, 0.005 and 0.007 and for Na_0.5Bi$_{0.5−x}$Sm$_{x}$TiO₃ samples 𝑥 is 0.05, 0.1 and 0.15. Dielectric constant and loss are studied in the frequency range 10 kHz to 1 MHz and in the temperature range $30–650^{\circ}$C. Impedance and electric modulus studies are undertaken. The relaxations observed in the samples are non-Debye and activation energies for relaxation and conduction are evaluated.