This paper provides a methodology for predicting post-transplant kidney function, that is, the 1-year post-transplant estimated Glomerular Filtration Rate (eGFR-1) for each donor-candidate pair. We apply customized machine-learning algorithms to pre-transplant donor and recipient data to determine the probability of achieving an eGFR-1 of at least 30 ml/min. This threshold was chosen because there is insufficient survival benefit if the kidney fails to generate an eGFR-1 ≥ 30 ml/min. For some donor-candidate pairs, the developed algorithm provides highly accurate predictions. For others, limitations of previous transplants' data results in noisier predictions. However, because the same kidney is offered to many candidates, we identify those pairs for whom the predictions are highly accurate. Out of 6977 discarded older-donor kidneys that were a match with at least one transplanted kidney, 5282 had one or more identified candidate, who were offered that kidney, did not accept any other offer, and would have had ≥80% chance of achieving eGFR-1 ≥ 30 ml/min, had the kidney been transplanted. We also show that transplants with ≥80% chance of achieving eGFR-1 ≥ 30 ml/min and that survive 1 year have higher 10-year death-censored graft survival probabilities than all older-donor transplants that survive 1 year (73.61% vs. 70.48%, respectively).