I still miss many of the animals I've known over the years (including one particular cat from the '60s!!!) But as the article points out, cloned animals have different personalities, and in that case (as I see it), they wouldn't be my original animal companion (although I would still love the clones).
I often clip some fur from a deceased animal and keep it before I bury them, and bury a little of my hair with them. It feels creepy and wierd and good and the right thing to do... all at the same time. (Okay, maybe not so wierd... ancient Egyptians and Vikings had some strange, if spectacular, ways of burying their dead. I can just imagine the response from onlookers if I gave one of my deceased animals a Viking-style sendoff at a nearby river, complete with a small floating watercraft in flames...)