The frequency and temperature dependence of the longitudinal proton relaxation time T-1 has been studied in liquid crystal droplets embedded in a solid polymer matrix in the nematic and isotropic phase over a broad Larmor frequency range (500 Hz less than or equal to nu(L) less than or equal to 84 MHz) employing the fast-field-cycling technique. The comparison of the droplet data, bulk 5CB data, and the pure polymer data show that T-1 is dominated by the cross relaxation at the liquid crystal-polymer interface in the entire frequency range. In the low frequency range (nu(L) less than or equal to 1 MHz), an additional relaxation process determines T-1 in both phases, namely reorientations mediated by translational replacements in the nematic phase and the exchange relaxation in the isotropic phase. The analysis of the cross relaxation rate k reveals that the simplified model of Vilfan is only applicable in the nematic phase and leads to an anchoring time tau(AS) of the molecules at the surface which is approximate to 1.3x10(-4) s, This model, however, cannot be applied in the isotropic phase, but must be extended by the spin diffusion time tau(p), which in this case determines the cross relaxation rate. The anchoring time tau(AS), which in the isotropic phase corresponds to the correlation time of the additional process, is much shorter than in the nematic phase, namely tau(AS)approximate to 10(-6) s.