Electron paramagnetic resonance spectroscopy of conduction electrons, i.e. Conduction Electron Spin Resonance (CESR), is a powerful tool for studies of carbon samples. Conductive samples cause additional effects in CESR spectra that influence the shape and intensity of the signals. In cases where conduction electrons play a dominant role, whilst the influence of localized paramagnetic centres is small or negligible, the effects because of the spins on conduction electrons will dominate the spectra. It has been shown that for some ratios of the bulk sample sizes (d) to the skin depth (δ), which depend on the electrical conductivity, additional size effects become visible in the line asymmetry parameter A/|B|, which is the ratio of the maximum to the absolute, minimum value of the resonance signal. To study these effects the electrical direct current-conductivity and CESR measurements are carried out for two amorphous bulk coal samples of anthracite and a higher anthraxolite. The observed effects are described and discussed in terms of the Dyson theory.