A guide to show first-time pet-owners how to cope with the death of their pet. It is never an easy time but it is important to give yourself the chance to grieve and to remember the good times you spent with your pet. Here are some tips to assist you in getting through the loss. Think of your new pet as a new being that your heart has room for. 2  Remember to take each day as it comes, as each day passes the grief lessens, but you will never forget the memories of your special pet. 3  Cry. 4  Let your tears and emotions out.