What do you do against nocturne?

As a Cassiopeia in mid you should certainly be saving Zonya's just for him, it also gives armor which will make you tougher. If you build a little HP(Cassiopeia does anyway) you should last long enough to use a Q to pop his spell shield. The moment he appears on your screen jumping towards you, you could Zonya's if you suspect this player blows his spell shield the moment he comes in, wait out the spell shield then ult him and use your Rylai's slow to run while gaining movespeed and healing yourself. Beyond laning try to stay very close to the best reflex CC champions on your team, it isn't surefire, but it increases your odds of him getting crowd controlled out of his assault, and might shift his focus to the ADC if they are less commonly near a tank.

For example or even can protect you well. Don't count on champions like or saving you, their forms of CC will not quickly stop his assault. It has to be somebody with fast acting hard CC.

If you are taking flash, you can also flash the moment he ults in, giving you some distance and cancelling his initial burst. If you are lucky his ult won't even do damage(it is bugged for a couple years now). If he is building enough AD to insta-gib you he will be pretty squishy so don't be afraid to duel him down.

The biggest threat is if his E goes off fully, you either have to get out of it, CC him right before it goes off, try to Zonya's it or try to kill him before it finishes. Once you are feared it is game over.

You could, and I don't entirely recommend this because Cass AP ratios are so low to compensate the 6th slot opened by boots. But you could troll him and go GA, just for lolz...

If your team isn't providing sufficient warding Noct will always be a threat, even if you do your best on your end. So if you have the ability to safely ward, do so. Also try buying control wards commonly to keep even more vision advantage. Knowing where he is(at least generally) is half the battle. Encourage in the friendliest way possible for your team to deep ward, like say "We need to keep track of Nocturne for ults, we should try warding around their jungle."

These are the tips I can offer. I don't know new Cass well, but I can offer those tidbits as somebody who use to play Nocturne.