For pilots, the capacity to cope with anxiety is crucial during a flight since they may be confronted with stressful situations. According to the Big Five Inventory, this capacity can be modulated by two important personality traits: conscientiousness and neuroticism. The former would be related to concentration skills and the latter to the attention bias towards anxiety-provoking stimuli. Given the current development of monitoring systems for detecting the users’ state, which can be incorporated into cockpits, it is desirable to estimate their robustness to inter-individual personality differences. Indeed, several emotion recognition methods are based on physiological responses that can be modulated by specific personality profiles. The personality traits of twenty pilots were assessed. Afterwards, they performed two consecutive simulated flights without and with induced social stress while electrodermal activity was measured. Their subjective anxiety was assessed before the second flight, prior to the stress-induced condition. The results showed that higher scores in neuroticism correlated positively with cognitive and somatic anxiety. Moreover, under social stress, higher scores in conscientiousness correlated positively with electrodermal stability, i.e., a lower number of skin conductance responses. These results on both self-reported and physiological responses are in favor of the integration of personality differences into pilots’ state monitoring.