This study investigates the feasibility of a dry electrode cap design for neonatal electroencephalogram (EEG) recordings. Recordings on a phantom and a real infant are compared between a novel dry electrode cap and a clinically used gel-based electrode cap. The phantom recordings included measuring both the electrode contact force and the signal quality during still and respiration-like head motion. The real infant recordings were assessed for the EEG signals' spectral characteristics, including powerline interference. Compared to gel-based caps, the dry caps showed a largely comparable skin force, an expectedly greater sensitivity to motion-induced artifacts, and a slightly lower powerline interference. Recordings on the real infant showed no significant skin marks after using the dry electrode, and the spectral compositions were comparable between dry- and gel-based electrode caps. These findings suggest that neonatal EEG recordings with a dry electrode cap are technically feasible, but movement-related artifacts, such as respiration in a supine lying infant, may challenge long-term recordings of spontaneous EEG activity. Yet, the ease of use of dry electrode caps calls for future studies to define the optimal use case in neonatal recordings.