Come down a few pegs

Come down a peg or two / Draw in one's horns / Be brought down a notch / Pull in one's ears / Come off one's perch / Eat crow / Eat humble pie / Get off one's high horse


Calare le arie

Abbassare la cresta / Abbassare le ali / Abbassare le penne


Meanings
Fig: to come to a humbler opinion of oneself; to lower one's self-esteem

Examples
My brother used to brag about his accomplishments in chess, but when the Russian champion came to town, he pulled in his horns and did a quick disappearing act
Mio fratello si vantava sempre delle sue vittorie a scacchi, ma quando ha saputo che il campione russo avrebbe giocato in città, ha abbassato la cresta ed è sparito dalla circolazione

Get over yourself, you jerk! Who do you think you are? You're certainly no better than us
Abbassa le ali! Chi ti credi di essere? Non sei certo meglio di noi

Mary was always boasting about all the boyfriends she could have, but she was brought down a peg or two when nobody invited her to the prom
Maria si è sempre vantata di poter avere tutti i ragazzi che voleva, ma ha dovuto calare le arie quando nessuno l'ha invitata alla festa di fine anno scolastico

Just because you've read a couple of books on ancient Greece, you pretend to be an expert in ancient history? Don't get too cocky! You still have a long way to go!
Solo perché hai letto un paio di libri sulla Grecia antica ti spacci per esperto di storia antica? Cala le arie! Ne hai di strada da fare!

Origin
Probably this expression originally referred to a ship's flag. Ship's flags were raised or lowered by pegs: the higher the position of the flag, the greater the honor.