The International Geomagnetic Reference Field (IGRF) is a set of parameters representing the large-scale internal part of Earth’s magnetic field. The 13th generation IGRF requested candidate models for a definitive main field for 2015.0, a provisional main field for 2020.0, and a predictive secular variation covering the period 2020.0–2025.0. The University of Colorado (CU) and the National Centers for Environmental Information (NCEI), part of the National Oceanic and Atmospheric Administration (NOAA), have produced these three candidate models for consideration in IGRF-13. In this paper, we present the methodology used to derive our candidate models. Our candidates were built primarily from Swarm satellite data, and also relied on geomagnetic indices derived from the ground observatory network. The ground observatories played a crucial role as independent data in validating our candidates. This paper also provides a retrospective assessment of the CU/NCEI candidate model to the previous IGRF (IGRF-12) and discusses the impact of differences between candidate and final IGRF models on global model errors.