I regularly play my friend's ZSS, and I don't have a whole lot of trouble with it. At the beginning of the match I try to disrupt her armor game by either lasering, or charging a gyro. As soon as they start tossing it, you can either spot dodge the first one, and shield the rest, or simply run away from it. The armor DOES hurt a lot, and can rack up a lot of damage, as well as give ZSS mobility that she normally wouldn't have. One match [which I have recorded I think] my friend jumped, and I shot my gyro right onto his armor which gave me enough time to steal it and kill him with it. But, I wouldn't count on that. Staying above ZSS is ridiculously bad, but I found out that your dair actually clanks with her UP-B, not that you will want to do that.
Also, if you pick up her armor, do not be afraid to toss it down and glide toss. It BOUNCES really high, so it can be used for setups, and you can usually recover it before it settles.
The number one thing to watch out for is her forward B, but it's pretty easy to dodge since it's so telegraphed. But her tilts and her jabs are excellent. Never ever get down smashed, it essentially is a free anything if it's charged a little.
That's about all I have to say about the match up. It's not the most fun [or maybe is], because you are both trying to do totally different things. ZSS is trying to combo you, and ROB is just trying to slow down the game so he can gain control over the field.