Background and Objectives: Early postoperative recovery after surgery is a key point for patients’ safety and comfort. Moreover, operating room turnover depends on recovery time. Our aim was to assess which method of remifentanil administration, manual (MI) or target-controlled infusion (TCI), could reduce patient time in recovery room. In this study, patients’ recovery times were registered and compared among the groups. Materials and Methods: We enrolled 31 morbidly obese patients in this prospective study. All of them had undergone bariatric surgery at the Hospital of Lithuanian University of Health Sciences Kauno Klinikos in 2020. Sevoflurane/remifentanil anaesthesia was performed for all patients. The patients were randomly assigned to the manual infusion (MI) (control group) or target-controlled infusion (TCI) group for the method of the administration of remifentanil. While the patients were waking up after the surgery, we recorded spontaneous breathing and airway reflexes recovery time, time of extubation, eye opening, recovery of orientation and beginning of the following oral command. For the TCI group, we also documented remifentanil concentrations in the blood (automatic infusion pump). Results: Patients did not differ in demographic values and duration of remifentanil infusion. We found that remifentanil consumption in the TCI group was lower, p = 0.02. Despite lower remifentanil consumption in the TCI group patients, they demonstrated longer total recovery time than the control group patiens: 14 (12–20) vs. 10 (6–16), p = 0.001. Conclusions: The study showed that, upon comparing the TCI method with MI, manual infusion produced better results in postoperative patient recovery. Additionally, higher doses of remifentanil were consumed using MI. In conclusion, the dosage recommended by highly qualified anaesthesiologists is favourable for morbidly obesity patients when compared to the TCI method.