A supernatural sense of smell seems to be as more keen by an order of magnitude, similar to a dog. Canine shapeshifters can track individuals via their scent, much like a bloodhound, and so they are effective trackers. They can also smell illness.
Their sense of smell can be so refined they are able to detect emotions - anger or fear. They do this by picking up chemosignals - chemical signals that communicate emotion, which an individual can give off via their scent, allowing them to identify the hormonal changes that person exhibits, or has exhibited at specific locations in the past.