Ancient and archival DNA samples are valuable resources for the study of diverse historical processes. In particular, museum specimens provide access to biotas distant in time and space, and can provide insights into ecological and evolutionary changes over time. However, archival specimens are difficult to handle; they are often fragile and irreplaceable, and typically contain only short segments of denatured DNA. Here we present a set of tools for processing such samples for state-of-the-art genetic analysis. First, we report a protocol for minimally destructive DNA extraction of insect museum specimens, which produced sequenceable DNA from all of the samples assayed. The 11 specimens analyzed had fragmented DNA, rarely exceeding 100 bp in length, and could not be amplified by conventional PCR targeting the mitochondrial cytochrome oxidase I gene. Our approach made these samples amenable to analysis with commonly used next-generation sequencing-based molecular analytic tools, including RAD-tagging and shotgun genome re-sequencing. First, we used museum ant specimens from three species, each with its own reference genome, for RAD-tag mapping. Were able to use the degraded DNA sequences, which were sequenced in full, to identify duplicate reads and filter them prior to base calling. Second, we re-sequenced six Hawaiian Drosophila species, with millions of years of divergence, but with only a single available reference genome. Despite a shallow coverage of 0.37±0.42 per base, we could recover a sufficient number of overlapping SNPs to fully resolve the species tree, which was consistent with earlier karyotypic studies, and previous molecular studies, at least in the regions of the tree that these studies could resolve. Although developed for use with degraded DNA, all of these techniques are readily applicable to more recent tissue, and are suitable for liquid handling automation.