Learn the player and their parry baits, watch to see if they bounce down or step forward after they perform a blocked string, you can tell what direction of parry they are trying to set up. Also there are common parry baits like Terry crackshoot, low parry, low forward, ARE YOU OK?! These tend to work well when the game is close because it is your natural reaction to try to punish/force them to block and it will come out without you knowing it… if the person knows you (and the game) more than you know them then you are in lots of trouble…
air throws do work really well too, because it gives you one more anti air option, and one that cant be parried at that (i know this was mentioned already). So when someone jumps you have normal anti air, specials (ie dragons) anti air - early, normal timing, and very deep (especially with cammy), poke them before they hit ground (ie, rolento c.jab), jumping air to air, super jumping air to air, jumping/superjumping air throw, low jump air to air… just gives you a lot of options if they jump in, gives them much more to think about.
changing up the timing of when you would attack (but not during poke strings, you dont want any gaps in your poke strings :D) but i mean like if they jump straight up or if like Gokou said always using the same move at the same distance right away (in any number of situations… like when you hit them air to air, and land next to them (and you didnt knock them down) this is a good time for them to low parry, if you stick out almost anything (even sagat standing jab!) you will eat a lot of damage)
but it comes down to a lot of outthinking… and sometimes this is very hard to do As depending on how many… damn, id like to quote sirlin but I forgot what he was talking about! The levels of counter actions you consider… and how many you think they are considering!
EDIT: An example of this is if they are expecting jump back strong, and you use fierce instead, which has slightly more startup and so the parrying is slightly different (assuming that they are trying to parry! them attacking is completely different situation… this is why p-groove is so frustrating! its that moment of Yes! I can hit them and gain momentum… oh wait I just got parried into super)