Any number of things could have caused the swans to leave your pond. The swans may have been looking for you, wanted more food and you were not around or were chased/scared by something, i.e. noise, dog, cat or humans.

If the other swan was going in a different direction, it probably is lost and does not know how to find its way home. Once the swan is located, you need to immediately capture it and return it to your pond. The swan that returned may walk to find the other swan So, it is very important they are reunited.

Lastly, because the swans are pinioned and cannot fly, they cannot escape predators and may be killed. For this reason, the location, capture and return of the swan to your pond ASAP is critical. Otherwise, the swan could be killed. Once the swans are returned to your pond, a fence to keep them in your pond is highly recommended. The Regal Swan