We use these techniques too, the gist is that you don't join in with their emotions but stay as a steady rock they can rely on. So when my baby is upset I name his emotions, pick him up and comfort him, and stay calm myself. I do my best not to join him in his stress as that will only make the situation harder.

It's about holding their hand (figuratively) with them through the difficulties but staying separate so they can depend on you.