emotions are felt when your body releases certain hormones. cats release hormones associated with emotions. ergo, cats have emotions. it's no more complicated than that, really.
however, there are plenty of observations you can use that are similar to the way you'd test a dog, you just need to have the same kind of behaviour enforced. if you have a cat that you walk, and it likes to walk, it will respond similarly to a dog if you say 'walk' or bring out the leash. you can shake the food box and see it react.
cats also display certain emotional traits that dogs don't. when they're angry with you, they'll turn their back to you and ignore you, for example. dogs may go and sulk, but they don't ignore you the same way.
www.xojane.com/fun/science-has-figured-out-dog-emotions-cat-emotions-remain-a-no-go