This depends on the reason for your cat being sick, however, it is likely that his stomach just needs to settle after being sick. If your cat has been poorly for sometime however, it is very important that they don't go for too long without food and especially water.
If your cat generally seems to be off food, why not try tempting your cat with a tin of tuna, something soft, easy to eat and very smelly so it tempts him to eat? Maybe some nice ham? Or warm chicken breast? Make sure that the food is mashed up and that there is nothing noisy like a washing machine or food mixer on nearby.
If your cat has a tender stomach, it might be a nice idea to elevate its food bowl with a few books so that it doesn't have to put any pressure on his tummy.
If you have recently deworming your cat, this could be down to
- The cat simply doesn't trust you after you gave it something horrible to eat!
- The worms are yet to be worked out of your cats' system.
If your cat is being sick regularly, please keep a not of what they are eating, are they and indoor or outdoor cat. What are their stools like, runny or solid? When they are sick is it just saliva and grass? This would be totally normal self cleansing mechanism that cats have. If any symptoms persist longer than 48 hours I would take the cat to the vet, cats can loose weight very quickly without eating, so try to get them to eat something at least.
Some cats simply eat their food too quickly and bring it back up again. A very disgusting habit some cats have, is to return to this regurgitated food and eat it again!
Just don't rush your cat into eating after being sick. They cannot communicate reasons to us, so we have to watch and try our best to guess what is wrong. Hairballs also play a factor, and it sounds awful when a cat brings one up, but again this is normal. Make sure you always have water down for the cat and if you need to better monitor its behaviour and it is a cat that normally goes outside, try to keep it indoors with a litter tray so that you can see what is happening with their stomach.