This is a perfectly correct and usable part of a sentence in written English
For example, "He responded with a gesture befitting the occasion." This phrase indicates that the response was appropriate for the situation.
The conversations were chaotic, befitting the scene.
The chill, befitting the mood, refused to lift.
As befitting the home of Mahatma Gandhi, Indian political leaders have great ambivalence about nuclear weapons.
Yankee Stadium feels stately and imperial, befitting the image of the team that plays there.
The collection became more dandified and genre-busting each year, befitting the label's name.
The day's hunt netted five lively articles, a typically contrary assortment befitting the BALSAM, JERRY brand.
As Marke, Matti Salminen, his mature voice sometimes hoarse, befitting the part, performed magnificently.
Befitting the scene's do-it-yourself attitude, the audience began the night's festivities.
Despite the exorbitant ticket prices, the Coliseum felt blue-collar, befitting the sport in question.
Several fans mentioned the unusually small desk in Prince's personal office, befitting the tiny musician's size.
They are very doggish, with serious, almost mask-like expressions, befitting the occasion.
