New DNA sequencing technologies are allowing researchers to explore the genomes of the millions of natural history specimens collected prior to the molecular era. Yet, we know little about how well specific next-generation sequencing (NGS) techniques work with the degraded DNA typically extracted from museum specimens. Here, we use one type of NGS approach, sequence capture of ultraconserved elements (UCEs), to collect data from bird museum specimens as old as 120 years. We targeted 5060 UCE loci in 27 western scrub-jays (Aphelocoma californica) representing three evolutionary lineages that could be species, and we collected an average of 3749 UCE loci containing 4460 single nucleotide polymorphisms (SNPs). Despite older specimens producing fewer and shorter loci in general, we collected thousands of markers from even the oldest specimens. More sequencing reads per individual helped to boost the number of UCE loci we recovered from older specimens, but more sequencing was not as successful at increasing the length of loci. We detected contamination in some samples and determined that contamination was more prevalent in older samples that were subject to less sequencing. For the phylogeny generated from concatenated UCE loci, contamination led to incorrect placement of some individuals. In contrast, a species tree constructed from SNPs called within UCE loci correctly placed individuals into three monophyletic groups, perhaps because of the stricter analytical procedures used for SNP calling. This study and other recent studies on the genomics of museum specimens have profound implications for natural history collections, where millions of older specimens should now be considered genomic resources.