Do things that your pet has all the time enjoyed, when still ready, like letting curling up on your lap for hours at a time, giving loads of time to roam in the yard, and consuming yummy little treats.
Establishing a memorial of some sort in honour of your pet (eg: a particular candle, a tree, a plaque) can also assist.
You can even dip your pets paw in a small bit of paint and place it on a piece of paper you could later display after the pet has died.
If you are depressing, your pets will react to it. Unlike a human being, who would possibly actually profit from understanding they are going to be missed and that their impending departure causes you a great deal of sorrow, your pet won’t perceive why you’re so sad – they may simply feel unhappy with you, or might even really feel they’ve performed something to upset you.