The desire to understand fish welfare better has led to the development of live monitoring sensor tags embedded within individuals for long periods. Improving and understanding welfare must not come at the cost of impaired welfare due to a tag’s presence and implantation process. When welfare is compromised, the individual will experience negative emotions such as fear, pain, and distress, impacting the stress response. In this study, Atlantic salmon (Salmo salar) underwent surgical implantation of a dummy tag. Additionally, half of this group was introduced to daily crowding stress. Both groups and an untagged group were followed for 8 weeks using triplicate tanks per group. Sampling took place once a week, and where stress was given, it was conducted 24 h before sampling. Stress-related measurements were taken to understand if tagging caused chronic stress and explore the chronic stress response and its impact on wound healing. Primary stress response hormones measured included CRH, dopamine, adrenocorticotropic hormone, and cortisol. Secondary stress response parameters measured included glucose, lactate, magnesium, calcium, chloride, and osmolality. Tertiary stress response parameters measured included weight, length, and five fins for fin erosion. Wound healing was calculated by taking the incision length and width, the inflammation length and width, and the inside wound length and width. The wound healing process showed that stressed fish have a larger and longer-lasting inflammation period and a slower wound healing process, as seen from the inside wound. The tagging of Atlantic salmon did not cause chronic stress. In contrast, daily stress led to an allostatic overload type two response. ACTH was elevated in the plasma after 4 weeks, and cortisol followed elevation after 6 weeks, highlighting a breakdown of the stress regulation. Fin erosion was elevated alongside cortisol increase in the stressed group. This data suggests that tagging previously unstressed fish in a controlled environment does not negatively affect welfare regarding stress responses. It also indicates that stress delays wound healing and increases the inflammatory response, highlighting how continued stress causes a breakdown in some stress responses. Ultimately, the tagging of Atlantic salmon can be successful under certain conditions where proper healing is observed, tag retention is high, and chronic stress is not present, which could allow for the possible measurement of welfare indicators via smart-tags.