Techniques that can be employed for saving face but maybe they could also be considered getting away with stuff.
Act innocent/ignorant, in most instances if you are a foreigner this will work. I.E. "You mean I shouldn't play drums with my chop sticks or stick them straight up in a rice bowl?" OOPS sorry, smoke in front of a public "no smoking" sign, etc.. IF you get called on it feign innocence and say "pie say"(sorry in Taiwanese) for the noobs. Mastering face is all about knowing what you want to do, get away with, or just don't want to do, and telling other people, "sorry" without ever saying sorry. The master of face never says sorry.
Tell someone you are going to do something but then don't do it. For example, you have a teaching contract that states you only work 16 hours per week for classroom teaching hour nothing else, The boss or future prospective employer asks or "wonders" (i.e. testing your ignorance) if you are willing to put in extra hours or to "make up" classes that other students missed... you say "I could do that"...but you won't. When they ask why you don't do the things they "wondered about" say I am really busy with (insert work, school, business, family member is sick, etc.) For the puritans you can be clever and make a truly honest answer like it isn't in my contract but you are putting yourself at a disadvantage after that point. Remember what you consider moral/ ethical is relative.
Same can go for correcting papers, judging speeches, etc, I could do it but I won't unless it is in writing. Don't forget that western rule of never signing anything unless you agree to it.
Walk away quickly. Turn your back and quickly move away from the situation, no interaction, no blame, no face.
NEVER EVER YELL or raise your voice UNLESS you are in a position of power/ authority. This means if you have the law/government/judge/regulations that are "being enforced" on your side you can yell. Only yell in a position of power. (If someone yells at you they either think they are "over you" or they are so upset they are ok with losing face). This especially applies in an environment with lots of people.
Cursing/ foul language in Taiwanese/Chinese, tolerable in a vechicle, in passing, or in traffic. Cursing someone in Taiwanese face to face is most likely going to begin a physical fight, see the one about walking away, People "walk away" every time they drive away from a scene.
Apologizing: It isn't really my fault but I am sorry that you "feel" that way. Never really apologize, because certainly if you never talked to this person it would have never happened. Therefore in some way your offense to them means that it would have never existed so it is partially your fault. Same applies for driving or automobile accidents, hence, the demand for money from a person who is not at fault.
Mindset: you exist, this happened, so you are at fault for existing, by being in my space.
Probably a reason why it is culturally acceptable to push "the backs of people" on mass public transportation, you exist, you are in my space, affecting me, move it! However you won't see a face to face push on the MRT, people exit properly without incident and people come in without incident. However the back pushing or mentally back stabbing is a game that takes finesse.
I am just citing a few examples/ techniques, there are plenty instances, techniques, examples...