It is always preferable for an owner to find a new home for a pet vs. placing the animal in a shelter. Life circumstances change and a responsible pet owner wants to make sure that his/her pet will be cared for by a responsible person. Shelters are overcrowded and there is no guarantee of an adoption. No-Kill shelters are particularly overcrowded as they have so many resident cats. If your pet was adopted from a shelter, be sure and call as many will take their own adoptions back. To increase your chances for finding a good home, make sure that your pet is spayed or neutered and in good health. Also, have your pet reasonably well groomed and assure the prospective adopter that your pet is house trained. You can advertise widely in web sites or set up a facebook page. There are general adoption websites such as http://www.petfinder.com. Give yourself plenty of time to place your kitty and use word of mouth with family and friends.