Udumaga, who can also play as a forward, has made three substitute appearances for the Bees in the Championship so far this season.
The 20-year-old also started the 4-0 Capital One Cup defeat by League Two side Oxford in August.
Ferry, 18, has yet to appear for Brentford's first team but has captained their development side.
Wycombe boss Gareth Ainsworth said: "We've got an excellent relationship with Brentford, which enables us to benefit from taking their youngsters on loan and contributing to their development on and off the pitch.
"James and Jermaine have played a lot of matches at youth level and we look forward to giving them the opportunity to experience a first-team environment in training and on matchdays."
Wycombe have signed midfielders James Ferry and Jermaine Udumaga on loan from Brentford until 23 December.