Magnetic stimulation of the brain.
Experiments have been done to use weak magnets on the head to try to evoke "mystical experiences", similar to those of some individuals, who have been able to strengthen their own faith, and partly served as a kind of merit for people who have come to serve as leaders of an organization or congregation. The results have been mixed. Granqvist (yy, referenced in Granqvist et al, 2014) has tested replicating these experiments with negative results.
Religious experiences are generally attributed great importance by religious themselves, as testimony that there exists a "spiritual dimension" in existence. This is regardless of whether it is the person himself or, for example, a spiritual authority who had them. Jaqueline Borg (yy?) at Karolinska Institutet has been researched on certain neurotransmitters that could possibly explain such "mystical experiences" in elevated doses.
A connection between the amount of serotonin receptors in the brain and openness to spiritual experiences etc (Borg). The difference here can be between different kinds of religiosity, rather than between religiosity in general and those who do not believe.