One of the recommendations I make to parents most often is to validate their child's emotions. I've recently heard it called "empathetic reflection" which is a term I like better.
It's the number one thing you can do to build your relationship with them, and for them to develop a strong sense of self, both of which are very strong predictors of mental health.
It's not always easy to do, and it's not to be confused with letting them do whatever they want! It needs to be combined with strong boundaries.
The three steps are
Say what you notice (eg "you didn't get chosen for the team")
Say what you think they might be feeling ("you might be disappointed"). This obviously has to be based on your intuition or some clue that they actually do feel this. Make sure this is not about what you feel or what you think they should feel. I quite like to say "some kids might feel...." to soften it and give the child an opportunity to correct me about their own experience.
STOP-do not try and fix their feelings
If they are talking about it, listen and repeat back to them what they say they are feeling, or what you think they might be feeling based on their body language or facial expression.
If they tell you they don't want to talk about it, let them know you're there if they change their mind, and don't say anything else.
If they say you've got it wrong, an apology might be appropriate and you can invite them to help you get it right.
Finally, emotionally validate positive emotions too!!
This is a good article about emotional validation