We present a newly developed microwave probe head that accommodates a gasketed sapphire anvil cell (SAC) for performing sensitive electron spin resonance (ESR) measurements under high-hydrostatic pressures. The system was designed around commercially available dielectric resonators (DRs) having the dielectric permittivity of approximately 30. The microwave resonant structure operates in a wide-stretched double-stacked geometry and resonates in the lowest cylindrical quasi TE(011) mode around 9.2 GHz. The most vital parts of the probe's microwave heart were made of plastic materials, thus making the resonant structure transparent to magnetic field modulation at 100 kHz. The overall ESR sensitivity of the probe was demonstrated for a small speck of 2,2-diphenyl-1-picrylhydrazyl radical (DPPH) positioned in the gasket of the SAC, using water as the pressure-transmitting medium. The system was also used for studying pressure-induced changes in spin-relaxation mechanisms of a quasi-1D-conducting polymer, K(1)C(60). For small samples located in the sample hole of the gasket the probe reveals sensitivity that is only approximately 3 times less than that yielded by regular ESR cavities.