We describe the coherent polarization transfer from an unpaired electron to neighboring nuclei via electron-nuclear cross polarization (eNCP) in a doubly, tilted rotating frame. Although the experiment superficially resembles the well-known Hartmann-Hahn cross polarization (CP) process introduced by Pines et al., that is widely used in solid-state nuclear magnetic resonance (SSNMR), it differs in significant respects. In particular, eNCP requires an alternative treatment due to the very different sizes of the specific terms in the spin Hamiltonian. We derive analytical expressions for the matching condition for optimal polarization transfer and verify their correctness with experimental results obtained with electron detected CP experiments performed on powder samples of BDPA radical dispersed in a protonated polystyrene matrix and with numerical simulations. We use fully protonated BDPA as an example of polarization transfer to strongly coupled nuclei. In contrast, perdeuterated BDPA serves as an example of the transfer of polarization from electrons to weakly coupled nuclei. In addition, we performed CP on a paramagnetic crystal to determine the influence of resolved hyperfine structure on the CP process. It is shown that almost no structure is observed in the corresponding electron-(1)H CP matching curve. It appears that only a restricted number of hyperfine coupled (1)H's contribute to the observed signal intensities in the CP experiment.