Background/Objectives: Anesthesia plays a very important role in the successful management of intraoperative neuromonitoring (IONM). The aim of our study was to investigate the impact of anesthesia induction and maintenance on the quality of signals during surgeries on the thyroid and parathyroid glands using neuromonitoring. Methods: The study included 72 patients who underwent surgery with IONM for one year. All the patients were intubated using a Glidescope videolaryngoscope with a hyperangulated blade. Two different approaches were used to facilitate intubation: succinylcholine-1 mg/kg and rocuronium bromide-0.3 mg/kg. For anesthesia maintenance, total intravenous anesthesia (TIVA) or combined anesthesia was used. Patients’ body movements during operations, as well as electromyography signals from the vagus and recurrent laryngeal nerves before resection, were recorded as V1 and R1. Results: Intraoperative unwanted movements were recorded in 25% of patients. Undesired movements were more frequently recorded in the TIVA group compared to the combined anesthesia group (p < 0.001) as well as in patients who received succinylcholine compared to patients who received rocuronium bromide (p = 0.028). Type of anesthesia maintenance as well as type of muscle relaxant did not affect the quality of recorded nerve signals. (p = 0.169 and p = 0.894, respectively). Conclusions: The type of muscle relaxant used significantly affects the occurrence of undesirable movements during thyroid surgery with IONM, while the type of anesthesia maintenance did not influence either the quality of the obtained signal or the occurrence of undesirable movements.