WordNet
matching funds
n. funds that will be supplied in an amount matching the funds available from other sources
Wikipedia
Matching funds
Matching funds are funds that are set to be paid in equal amount to funds available from other sources. Matching fund payments usually arise in situations of charity or public good. The terms cost sharing, in-kind, and matching are often used interchangeably.
Usage examples of "matching funds".
It appeared that he would not get the 5 percent necessary to receive federal matching funds in the next election.
Subsequent payments to Palladino - including federal matching funds - were even larger.