poised The Free Dictionary
self-possessed; dignified; exhibiting composure....self assured
Someone who is immune to embarrassment is poised, or has poise. Example, from The House of Seven Gables by Nathaniel Hawthorne:
But what was most remarkable, and, perhaps, showed a more than common poise in the young man, was the fact that, amid all these personal vicissitudes, he had never lost his identity.
The meaning of poise that I am using in this answer dates from the 1640s, according to Etymonline; the ballerina's poise on-stage (mentioned in one of the comments, below) is more than 100 years later.
The sense of "steadiness, composure" first recorded 1640s, from notion of being equally weighted on either side (1550s). Meaning "balance" is from 1711; meaning "way in which the body is carried" is from 1770.