Many studies have investigated the state of the health of healthcare workers during the acute period of the pandemic. Yet, few studies have assessed the health of such professionals after the pandemic and in a less dramatic period. This study involved a particular sample represented by residents in anaesthesia–resuscitation and psychiatry at a university in northern Italy particularly affected by the pandemic. The objectives were to investigate some indicators of health and well-being and compare the two groups of trainees. Using Google Forms, the following tests were proposed: the General Health Questionnaire, Maslach Burnout Inventory, Subjective Happiness Scale, Satisfaction with Life Scale, Coping Inventory for Stressful Situations, Brief Resilience Scale, State-Trait Anxiety Inventory, as well as an ad hoc questionnaire. A qualifying element of the work was the discussion of the results with the trainees. Various strengths have emerged, such as high values of resilience and job satisfaction; a positive assessment of the support received from the work team; an articulate use of coping strategies; and good levels of happiness and satisfaction with life, in both specialities. However, a widespread anxiety also emerged, which appears to be more attributable to concerns about professional evaluation, rather than the pandemic itself. In summary, the trainees seem to have found a fair amount of personal balance, whereas the relationship with the patient seems to be more compromised. In the comparison between specialities, the only significant differences are the levels of depersonalisation and resilience, both of which are higher in anaesthetists.