I still haven't read "How Animals Grieve" but just saw a good example. Someone shared a video of a mother sea lion grieving over the dead body of her baby. She moans, touches her baby, and cries. So this is how this particular sea lion grieves.
(I was going to share a link to the video but thought better of it just now. I wouldn't want someone recording and sharing images of me crying over a dead loved one.)