Reticulate evolution, in which phylogenetic relationships are not strictly bifurcating (tree-like), is a common feature of fern evolution. Ferns are prone to hybridization and whole genome duplication, two processes that can make untangling phylogenetic relationships among species challenging. Next-generation sequencing technologies have greatly increased the amount of data available for analyzing various aspects of evolutionary history, and here we test the ability of one next-generation sequencing approach to identify the progenitors of allopolyploids. We produced and analyzed double-digest restriction-site-associated DNA (ddRAD) sequences from six species of North American Dryopteris, including two allopolyploids and their respective diploid parents. The relationships of these species have been confidently established in previous studies, and our goal was to determine the extent to which RAD data are capable of identifying these known relationships. Analyses of the genetic structure in our samples reliably separated the diploids from one other, but in general each polyploid sample resembled one or the other of its progenitors, or had genetic variation unassignable to either parent. None of the polyploid samples had unambiguous genetic contributions from both known parents, as we had expected. These results may have been influenced by small overall sample size, different numbers of samples from the two diploid parents in each pair, and the large divergence times between the diploids. These are all potentially important issues to consider when designing similar studies, and our results therefore have useful implications for researchers interested in using a RAD approach to study polyploid complexes.