The genetic underpinnings of most pediatric-cancer cases are unknown. Population-based studies use large sample sizes but have accounted for only a small proportion of the estimated heritability of pediatric cancers. Pedigree-based studies are infeasible for most human populations. One alternative is to collect genetic data from a single nuclear family and use inheritance patterns within the family to filter candidate variants. This approach can be applied to common and rare variants, including those that are private to a given family or to an affected individual. We evaluated this approach using genetic data from three nuclear families with 5, 4, and 7 children, respectively. Only one child in each nuclear family had been diagnosed with cancer, and neither parent had been affected. Diagnoses for the affected children were benign low-grade astrocytoma, Wilms tumor (stage 2), and Burkitt's lymphoma, respectively. We used whole-genome sequencing to profile normal cells from each family member and a linked-read technology for genomic phasing. For initial variant filtering, we used global minor allele frequencies, deleteriousness scores, and functional-impact annotations. Next, we used genetic variation in the unaffected siblings as a guide to filter the remaining variants. As a way to evaluate our ability to detect variant(s) that may be relevant to disease status, the corresponding author blinded the primary author to affected status; the primary author then assigned a risk score to each child. Based on this evidence, the primary author predicted which child had been affected in each family. The primary author's prediction was correct for the child who had been diagnosed with a Wilms tumor; the child with Burkitt's lymphoma had the second-highest risk score among the seven children in that family. This study demonstrates a methodology for filtering and evaluating candidate genomic variants and genes within nuclear families that may merit further exploration.