Chemical immobilization is necessary for the physiological study of large wild animals. However, the immobilizing drugs can adversely affect the cardiovascular and respiratory systems, yielding data that do not accurately represent the normal, resting state. We hypothesize that these adverse effects can be ameliorated by reversing the immobilizing agent while holding the animal under general anaesthesia. We used habituated sheep Ovis aries (N = 5, 46.9 ± 5.3 kg body mass, mean ± SEM) and goats Capra hircus (N = 4, 27.7 ± 2.8 kg) as ungulate models for large wild animals, and measured their cardiorespiratory function under three conditions: (1) mild sedation (midazolam), as a proxy for the normal resting state, (2) immobilization (etorphine and azaperone), and (3) general anaesthesia (propofol) followed by etorphine antagonism (naltrexone). Cardiac output for both sheep and goats remained unchanged across the three conditions (overall means of 6.2 ± 0.9 and 3.3 ± 0.3 L min, respectively). For both sheep and goats, systemic and pulmonary mean arterial pressures were significantly altered from initial midazolam levels when administered etorphine + azaperone, but those arterial pressures were restored upon transition to propofol anaesthesia and antagonism of the etorphine. Under etorphine + azaperone, minute ventilation decreased in the sheep, though this decrease was corrected under propofol, while the minute ventilation in the goats remained unchanged throughout. Under etorphine + azaperone, both sheep and goats displayed arterial blood hypoxia and hypercapnia (relative to midazolam levels), which failed to completely recover under propofol, indicating that more time might be needed for the blood gases to be adequately restored. Nonetheless, many of the confounding cardiorespiratory effects of etorphine were ameliorated when it was antagonized with naltrexone while the animal was held under propofol, indicating that this procedure can largely restore the cardiovascular and respiratory systems closer to a normal, resting state.