1) Allow children to have their feelings so they can learn they are capable of dealing with them.I'd also add that allowing children to have their feelings gives them stronger experience of unconditional love. At young ages it is difficult to impossible for a child to separate their self-concept from their experiences and what you tell them about themselves through direct and indirect messages. Therefore, they receive your acceptance of their emotions deep in their soul as acceptance of them as a person. They learn they are still loveable when they are angry, sad, or having other big feelings. Sending them away to calm down gives the message that happy is the only acceptable emotion.
2) Don't rescue or try to talk children out of their feelings.Rescuing or trying to talk children out of their feelings sends the message that big feelings are too big and scary for you to handle and therefore too big and scary for them to handle.
3) Validate their feelings: "I can see you are really (angry, upset, sad)."This statement is actually reflective instead of validating. According to this article to be truly validating, a response to emotions needs to communicate this message:
"Your feelings make sense. Not only do I hear you, but I understand why you feel the way you do. You are not bad or wrong or crazy for feeling the way you do."
"It makes sense that you feel that way," or "I'd be (angry, upset, sad) too," can be helpful additions to fully validate emotions. And, to make it trickier, unless it comes from a place of true empathy, such statements may make your child feel condescended to and manipulated. You can make sure your response does come across with empathy by allowing yourself to imagine yourself in the same or similar situation before speaking.
4) Then keep your mouth shut and have faith in you children to work it through.I'd add, remain present and available if they want to talk it out, need a hug, etc. Unless they specifically ask for or demonstrate a need for space, your presence and availability communicates your fundamental acceptance and unconditional love for them, no matter what they are feeling.