Active sampling in the olfactory domain is an important aspect of mouse behaviour, and there is increasing evidence that respiration-entrained neural activity outside of the olfactory system sets an important global brain rhythm. It is therefore important to accurately measure breathing during natural behaviours. We develop a new approach to do this in freely moving animals, by implanting a telemetry-based pressure sensor into the right jugular vein, which allows for wireless monitoring of thoracic pressure. After verifying this technique against standard head-fixed respiration measurements, we combined it with EEG and EMG recording and used evolving partial coherence analysis to investigate the relationship between respiration and brain activity across a range of experiments in which the mice could move freely. During voluntary exploration of odours and objects, we found that the association between respiration and cortical delta and theta rhythms decreased, while the association between respiration and cortical alpha rhythm increased. During sleep, however, the presentation of an odour was able to cause a transient increase in sniffing without changing dominant sleep rhythms (delta and theta) in the cortex. Our data align with the emerging idea that the respiration rhythm could act as a synchronising scaffold for specific brain rhythms during wakefulness and exploration, but suggest that respiratory changes are less able to impact brain activity during sleep. Combining wireless respiration monitoring with different types of brain recording across a variety of behaviours will further increase our understanding of the important links between active sampling, passive respiration, and neural activity.