There are many parallels between historical linguistics and molecular phylogenetics. In this paper we describe an algorithmic pipeline that mimics, as closely as possible, the traditional workflow of language reconstruction known as the comparative method. The pipeline consists of suitably modified algorithms based on recent research in bioinformatics, which are adapted to the specifics of linguistic data. This approach can alleviate much of the laborious research needed to establish proof of historical relationships between languages. Equally important to our proposal is that each step in the workflow of the comparative method is implemented independently, so language specialists have the possibility to scrutinize intermediate results. We have used our pipeline to investigate two groups of languages, the Tsezic languages of the Caucasus and the Mataco-Guaicuruan languages of South America, based on the lexical data from the Intercontinental Dictionary Series (IDS). The results of these tests show that the current approach is a viable and useful extension to historical linguistic research.