I can attest that the absolute best way to cope with the grief over a lost pet is to rescue another.
I’ve heard it said that grief is just love with no place to go. When the pet that you loved so much crosses the rainbow bridge, the best place for all that love to go is to a previously unloved dog or cat (or gerbil or hamster or hedgehog or whatever else).
My story is that I went into the animal shelter looking to find a Lucy Jr, but got picked by an unexpected (and polar opposite in many ways) tortie feline.
All I can say is that you will know when you find the right one. More often than not, he or she will be the one to pick you, not the other way around.
Even if you haven’t recently lost a pet, it’s still a good thing to rescue an animal. There’s no more loving and loyal pet than a rescue.