Patients with hypoplastic left heart syndrome who have been palliated with the Fontan procedure are at risk for adverse neurodevelopmental outcomes, lower quality of life, and reduced employability. We describe the methods (including quality assurance and quality control protocols) and challenges of a multi-center observational ancillary study, SVRIII (Single Ventricle Reconstruction Trial) Brain Connectome. Our original goal was to obtain advanced neuroimaging (Diffusion Tensor Imaging and Resting-BOLD) in 140 SVR III participants and 100 healthy controls for brain connectome analyses. Linear regression and mediation statistical methods will be used to analyze associations of brain connectome measures with neurocognitive measures and clinical risk factors. Initial recruitment challenges occurred that were related to difficulties with: (1) coordinating brain MRI for participants already undergoing extensive testing in the parent study, and (2) recruiting healthy control subjects. The COVID-19 pandemic negatively affected enrollment late in the study. Enrollment challenges were addressed by: (1) adding additional study sites, (2) increasing the frequency of meetings with site coordinators, and (3) developing additional healthy control recruitment strategies, including using research registries and advertising the study to community-based groups. Technical challenges that emerged early in the study were related to the acquisition, harmonization, and transfer of neuroimages. These hurdles were successfully overcome with protocol modifications and frequent site visits that involved human and synthetic phantoms.