Is there a word that describes the swift and skillful covering of the natural emotions?
Solution 1:
Usually I'd say, "they had a good poker face."
poker face (plural poker faces) (poker)
An impassive facial expression cultivated to prevent other players from determining whether one's actions in the game are the result of a quality hand, or of bluffing.
Any similar expression used to prevent giving away one's motives, feelings, or situation.
Edit: It has been brought to my attention that I failed to cite the above c&p. The definition is from Wiktionary
Solution 2:
You might consider composed
free from agitation : calm; especially : self-possessed
He had told us he felt nervous about the performance, but he seemed perfectly composed when he walked onto the stage.
Note that composed does not necessarily mean an appearance that is at odds with the person's true emotional state.
Similarly you might consider self-possessed
having control of one's emotions, etc
SUPPLEMENT
On second thought, perhaps the verb mask applies
To conceal one's real personality, character, or intentions.
You could say, To calm their children, the parents masked their fear of the marauding bear.