The maximum amount of tuition assistance you can receive under the Post 9/11 GI Bill is equal to the tuition of the most expensive public institution in your state. If you would like to attend a private institution that is more expensive, then the institution must participate in the "Yellow Ribbon Program." The Yellow Ribbon Program will allow veterans to attend any institution, even if the tuition is higher than the maximum state tuition for that state.
For example: Matt decides he wants to attend Yale, a private university whose tuition is significantly higher than the public schools in Connecticut. If the highest in-state tuition in Connecticut is $4,000, and the tuition for Yale is $10,000, then the post 9/11 GI Bill can only pay $4,000 toward the Yale tuition. The Yellow Ribbon Program will require Yale to offer the student a scholarship for at least half of the difference, with the VA agreeing to pay the other half. In this instance, the post 9/11 GI Bill will provide $4,000, Yale will supply a $3,000 scholarship, and the VA will match the school with an additional $3,000, in order to completely pay for Matt's tuition.
The Department of Veteran Affairs will handle the process of coordinating the Yellow Ribbon Program with your private institution of choice.