Federated learning (FL) is a paradigm that allows distributed clients to learn a shared machine learning model without sharing their sensitive training data. However, for a successful and credible federated learning system, parties must be incentivized according to their contribution. Federated learning architectures require resources to fund a central server and, depending on the use-case, reimburse clients for their participation. While the problem of distributing resources to incentivize participation is important, a sustainable system first needs to get such resources. We propose a federated learning system (Federated Incentive Payments via Prior-Free Auctions, FIPFA) in the semi-honest trust model that can collect resources from self-interested clients using insights from prior-free auction design. Our system works even if clients are willing to make monetary contributions of differing amounts in exchange for high-quality models, and the server has no prior knowledge of these preferences. We run experiments on the MNIST dataset to test the model quality and incentive properties of our system.