First of all, my heartfelt sympathy for your loss. My cat passed just a little over a year ago and my heart remains broken. I have a new cat now that I have had for about 6 months and she is a sweetheart, so she helps fill the void because she is so wonderful and has some similar traits - mostly a very pleasing personality - to my cat who passed away.
Grief is a very personal journey. The only way out is through. I think the best way to cope is to just feel your grief and express it in a way that works for you. Some people talk to friends; others prefer not to talk about their loss. You may want to look at other cats and you may not. Perhaps you want to set up some kind of memorial to your cat such as a donation to a local shelter or rescue organization.
I still have my cats ashes - I have not decided where to sprinkle them, but I think it is good to have some closure of some kind and I plan to sprinkle them soon, now that warmer weather is here again. Perhaps in a garden in a park...
You may want to look for a grief support group or find books about grief that help reassure you that what you are feeling is normal.
You may want to make a box of memories - photos of your cat, etc. If you haven't got a framed photo of your cat out, you may want to have one made to place where you can look at it every day and remember your cat.
Everyone grieves differently. I hope you find what works for you, and again, my deepest sympathy.