The results of studying the dielectric permittivity, the third harmonic coefficient, and the DTA signal for Al2O3 nanoporous matrices filled with rubidium nitrate are presented. A shift of the phase transition Tc ≈ 437 K by 3 K to the low-temperature region and an increase in the temperature hysteresis of the phase transition from 14 K for polycrystalline RbNO3 to 33 K for RbNO3 in the pores of the Al2O3 oxide film were found.