Nasal airflow plays a critical role in olfaction by transporting odorant from the environment to the olfactory epithelium, where chemical detection occurs. Most studies of olfaction neglect the unsteadiness of sniffing and assume that nasal airflow and odorant transport are “quasi-steady,” wherein reality most mammals “sniff.” Here, we perform computational fluid dynamics simulations of airflow and odorant deposition in an anatomically accurate model of the coyote (Canis latrans) nasal cavity during quiet breathing, a notional quasi-steady sniff, and unsteady sniffing to: quantify the influence of unsteady sniffing, assess the validity of the quasi-steady assumption, and investigate the functional advantages of sniffing compared to breathing. Our results reveal that flow unsteadiness during sniffing does not appreciably influence qualitative (gross airflow and odorant deposition patterns) or quantitative (time-averaged olfactory flow rate and odorant uptake) measures of olfactory function. A quasi-steady approximation is, therefore, justified for simulating time-averaged olfactory function in the canine nose. Simulations of sniffing versus quiet breathing demonstrate that sniffing delivers about 2.5 times more air to the olfactory recess and results in 2.5–3 times more uptake of highly- and moderately-soluble odorants in the sensory region per unit time, suggesting one reason why dogs actively sniff. Simulations also reveal significantly different deposition patterns in the olfactory region during inspiration for different odorants, and that during expiration there is little retronasal odorant deposition in the sensory region. These results significantly improve our understanding of canine olfaction, and have several practical implications regarding computer simulation of olfactory function.