New EPR resonators were developed by using a ceramic material with a high dielectric constant, epsilon=160. The resonators have a high quality factor, Q=10(3), and enhance the sensitivity of an EPR spectrometer up to 170 times. Some advantages of the new ceramic resonators are: (1) cheaper synthesis and simplified fabricating technology; (2) wider temperature range; and (3) ease of use. The ceramic material is produced with a titanate of complex oxides of rare-earth and alkaline metals, and has a perovskite type structure. The resonators were tested with X-band EPR spectrometers with cylindrical (TE(011)) and rectangular (TE(102)) cavities at 300 and 77K. We discovered that EPR signal strength enhancement depends on the dielectric constant of the material, resonator geometry and the size of the sample. Also, an unusual resonant mode was found in the dielectric resonator-metallic cavity structure. In this mode, the directions of microwave magnetic fields of the coupled resonators are opposite and the resonant frequency of the structure is higher than the frequency of empty metallic cavity.