agree with mtf, jm, ml. But you MUST be consistent, otherwise you are teaching them that all they need to do to get their way is to throw a BIGGER tantrum - because at some point, eventually mummy will (or might) give in. That does not help them or you
If it distresses you, then leave the room or have your "time out" area in another room where your child is safe, but you don't have to be too close to their upsets. Also deal with it without showing that you are upset
I agree with picking your battles though, and although you need to be consistent with your timeout, there will be times when you can quite successfully distract them before a melt down or other bad behaviour occurs, to avoid having to use timeout. for example, when ds doesn't want to go to bed, we "race him" there, or let him ride on "mummy horse" (mummy on crawling with ds on my back like a horse) - this distracts him and he has fun joining in and he forgets his objections and is soon doing what we want without even complaining.
I have also found that confirming that you understand what the child wants helps (because they get frustrated at their inability to communicate). So if we are leaving the swiming pool and ds gets sad, I say "I know that you want to swim some more, but it is time to go. We will come back again soon". This has had AMAZING results. I am not debating with him or anything, but am saying that I understand what he wants (even though he is not going to get it).
Another thing that really works for us is giving them a choice (as in, "you can either sit in your booster chair, or you can go to time out"). they mostly (but not always choose to do the thing you want them to do = but sometimes they choose timeout, and if they do, then at least they know they have a choice and they must live with the consequences of their behaviour). After they've done time out, offer them the choice again, and they might choose more wisely. Also, I find that other types of choices also make them feel empowered. For example, if they don't want to put their pajamas on, then I might let them choose which pajamas they want to wear (but they get the message that they cannot choose whether or not to wear pajamas - just which ones they want to wear). This also makes them feel empowered.
The most important thing is consistency, though
Good luck!!