The relevance of formal hypnotic induction to the experience of trance and its neural correlates is not clear, in that hypnotizability, beliefs and expectation of hypnosis may play a major role. The aim of the study was assessing the EEG brain activity of participants with high (highs) or low hypnotizability scores (lows), aware of their hypnotizability level and informed that the session will include simple relaxation, formal hypnotic induction and neutral hypnosis. A total of 16 highs and 15 lows (according to the Stanford Hypnotic Susceptibility Scale, form A) were enrolled. Their EEGs were recorded during consecutive conditions of open/closed-eyes relaxation, hypnotic induction, neutral hypnosis and post hypnosis not interrupted by interviews. The studied variables were theta, alpha and gamma power spectral density (PSD), and the Determinism (DET) and Entropy (ENT) of the EEG signal Multidimensional Recurrence Plot (mRP). Highs reported significantly greater changes in their state of consciousness than lows across the session. The theta, alpha and gamma PSD did not exhibit condition-related changes in both groups. The Alpha PSD was larger in highs than in lows on midline sites, and the different sides/regions’ theta and gamma PSD were observed in the two groups independently from conditions. ENT showed no correlation with hypnotizability, while DET positively correlated with hypnotizability during hypnosis. In conclusion, the relevance of formal hypnotic induction to the experience of trance may be scarce in highs, as they are aware of their hypnotizability scores and expecting hypnosis. Cognitive processing varies throughout the session depending on the hypnotizability level.