Most separated sauces can be fixed. Even a broken hollandaise can be fixed if the fat is separated from the other liquid, instead of having the smooth consistence of a good emulation.
However, let’s take exceptions first: Sauces with eggs, like all hollandaise derivate are easily ruined by excessive heating. The tips to fix broken sauce do exclude sauces where hard-boiled eggs are included, but no emulations where eggs are whipped or stirred in, such as béarnaise sauce and hollandaise. If those are heated up too much, the protein in the egg is cooked solid, and the sauce can’t be saved.
Too much heat applied is also going to curdle yolks, ruining the sauce.
If the sauce has separated, for instance if you have added too much fat at once, it is easily saved:
Whisk together one egg yolk and a tablespoon of water. Add it to the broken sauce, just a little at a time while you stir vigorously all the time. This should fix most separated hollandaise based sauces.
A sauce that separate because of too much lemon, vinegar or wine, or because it has been boiling for a long time, can usually be smoothed again. Create a new thickening and add it to the broken sauce. Again, it is important to stir constantly and only add a little at a time so you don’t make lumps during the rescue attempt.
One more tip, if you promise not to tell anyone where you got it: If you are serving only yourself or your forgiving family, and don’t have time to make a new sauce, you may revert to the brute force approach. Keep the mixer deep in the sauce, trying not to blend air. You may be able to eat the result…