Birds do not have a great sense of smell in relation to other senses. Therefore, we would doubt that they recognize the young by smell. More than likely, it is through sight and sound. The cygnets constantly peep in order to let their mother know that they are okay as well as their location. So, the parents probably recognize their specific sounds.

Additionally, some research proposes that the uropygial oil gland (preen gland) has the specific purpose of feather health, water repellency, and ultraviolet attributes. The ultraviolet theory is that when the oil is rubbed over the swan's eyes, it provides an ultraviolet feature that allows the swans to recognize other individual swans. The Regal Swan