If you have searched for a long time, and when you start to feel the time is right, it can help to think of a "closure date". This is a date when you give yourself permission to "close off" your search. It could be months away from now, but it gives you (and your family) an end point. Only you will know when that time feels right for you.
As you approach your pre-decided "closure date", start to think about how you may want to use that time that will be freed once you’re no longer doing the flier drops, door knocks and internet searches. Even the time you spend worrying. What will you replace that time with? What will you do with that time that’s positive for you and moves you forward?

Then give yourself time and space to grieve their loss.
Helping children to grieve
While we are dealing with our own grief, our children are grieving too. Help your child with these new feelings during this time. Validate their how they feel by acknowledging them and naming the emotion you see, for example if a child is looking sadly at their lost cat Gizmos picture, say “I can see you’re feeling really sad about Gizmo”. We don’t need to try to change those feelings. Their feelings are valid and real. We just need to hear them and accept them. We adults can’t “fix” this for our children or protect them from this. But we can be there with them, with a hug, or let them cry. Or cry together….
Making a memory book
Children (and adults) may find making a memory book about their pet helps. A special book could include pictures, their adoption certificate and stories such as how you met your pet, fun times you shared, family holidays together etc.
Pay it forward in memory of your pet
Some people choose to volunteer to help pets as a tribute to their own pet. A lovely lady named Belinda volunteered to help Petsonthenet for several years, uploading all our SPCA found ads in memory of her own cat. She did this because it helped her to heal and "give back" in his memory and to help others in her situation.
Others may choose to help with appeal collecting, fundraising or fostering kittens or puppies. Many shelters such as SPCA welcome volunteers for a wide array of work for only a few hours a week.
Considering a new pet
For many of us the thought of living without the purr of a cat or the companionship of a dog is unthinkable, so a time will come eventually when you start to feel it might be time to welcome a new pet into your family.
Give this the amount of time that feels right for you to accept and grieve your loss before you move on. Keep in mind that if your pet does come home and finds an "interloper" in their place, that could go down badly with one or both pets. Unfortunately, I have seen this happen several times. Sometimes the two pets were not prepared to share their family, so one or even both wander off and become lost again. Sometimes they fight leading to injuries and vet bills, with the more submissive pet ending up living a sad life hiding under the bed all day. In other cases families have found themselves with more pets than they could manage financially or time-wise. This sometimes left them in the difficult position of choosing which pet to rehome, the old one, or the new one…. Try to avoid these issues by allowing enough time to be fairly sure this won’t happen. With cats, my experience is this is ideally at least six months. After that time it becomes less likely a lost cat will be found. However I have definitely seen many cats found after a year or longer, though that is far less likely. So six months seems a good compromise period based on probability.
Sometimes children will start asking for a new pet very quickly, which is completely understandable as they simply miss the joy and friendship of their pet. Personally, for our family, we see a valuable life lesson for our kids to help them understand that a pet is not a commodity that can simply be replaced. For the same reason we would not adopt an identical pet because it would be too easy for children (and even us!) to see it as the "same" pet, just living on forever through "new versions". Although quick replacement or an identical pet may save children pain in the short term, it doesn’t help them learn to understand and cope with important losses in their life. Although it is hard for everyone, ultimately this is a gift to our children which will make them stronger and more emotionally resilient as adults.
More help
Skylight provides New Zealand based grief support and specialist resources to children, teens, adults and their families and friends who are impacted by any kind of grief - whatever the cause, whatever their age, and wherever they live in New Zealand.
There is a special pet grief section at https://skylight.org.nz/Pet+Loss which mainly covers the death of a pet, but many of the resources are also useful for unresolved pet loss with excellent suggestions on how to make a memory book etc.
Take care of yourself
Please take care of yourself, eat well, rest and surround yourself with positive supportive people.
Know that it’s OK to love another pet again, when you ready and when the time is right.