We always stuck to our guns. Sometimes we could cajole our boys out of a tantrum by saying "Do you think if you yell and scream lonud enough I'll change my mind? Go on, give it a try!" They would scream louder, I would look throughtful, then say "Nope, didn't work". Of course I would never do that with a serious tantrum - the timing had to be just right.
But by being consistent, and NOT changing our minds, our sons eventually learned that tantrums do not get them what they want, and they stopped having them.
Menawhile, what we did when a child was having a fit was to put him in another room - not a time-out - the child could come out of the bedroom as soon as he felt in control enough to stop screaming (sometimes that happened immediately, sometimes it took longer). The philosophy at our house is that you are entitled to have a fit, but the rest of the family isn't obligated to listen to it. I would carry him to a bedroom, and ask "Lights on or off? Door open or closed? Sit on the bed or on the chair?" I think having control over those little decisions helped him feel like maybe he had some control in his life after all. After a few minutes I would go in, and if he wanted me to stay, I would. But if he came out of the room still screaming and crying, I would carry him back, and tell him he could come out and join the rest of the family when he was ready to stop crying.
Usually he would come bouncing out of the room a few minutes later, like a light switch had been turned off - smiling, cheerful, ready to move on.