Dry-contact electrodes are increasingly being used for EEG recordings in both research studies and consumer products. They are more user-friendly and better suited for long-term recordings. However, dry-contact electrodes also bring challenges with respect to the stability and impedance of the electrode-skin interface. We propose a methodology to characterize and compare dry-contact electrodes. The characterization is based on measuring the electrode-skin impedance spectrum, fit a parametric model of the electrode-skin interface to the measured spectrum, and calculate the resulting thermal noise spectrum. Thereby it is possible to relate the noise of an EEG recording to the theoretical noise contribution from the electrode-skin interface. To demonstrate the methodology, we performed an empirical study comparing two types of dry-contact electrodes in an ear-EEG setup. The electrodes were IrO2, previously used for ear-EEG, and a new design based on Ag/AgCl. Here, we related the noise floor of an auditory steady-state response (ASSR) to the thermal noise spectrum of the electrode-skin interface. The study showed similar impedance and EEG recording quality for the two electrode types, and the thermal noise of the electrode-skin interface was below the noise floor of the EEG recordings for both electrode types. Dry-contact EEG is an enabling technology for long-term brain monitoring of patients. This may be relevant for example for monitoring of neurodegenerative diseases, stroke patients, patients with traumatic brain injuries, and psychiatric patients.