Idiomatic expression meaning to not reveal emotions

Solution 1:

In American English, we often call this having a "deadpan" expression:

deadpan adj
Impassively matter-of-fact, as in style, behavior, or expression: deadpan delivery of the joke.

TFDO

Etymonline gives this origin:

1928, from dead (adj.) + pan (n.) in slang sense of "face."

So it arrives via a description of an absolutely lifeless expression, giving nothing away.

Solution 2:

As you say, Poker face is the best. It can be used as the object in a sentence:

"He wore / put on / displayed his best poker face during the trial."

Solution 3:

No one has suggested keep a stiff upper lip yet. It's not an exact match (may not apply to all emotions), but can work in certain contexts.

stiff upper lip: self-restraint in the expression of emotion (especially fear or grief)

(WordNet)

Example: When she heard the bad news, she kept a stiff upper lip.