In many simultaneous localization and mapping (SLAM) systems, it is desirable to exploit the fact that the system is traversing though a previously visited environment. Once these locations, commonly known as loop closures, have been detected the system must be able to both compute and verify the relative transformation between proposed locations. In this thesis we present two independent algorithms, using 2D LiDAR scanners, for robustly computing the transformation between arbitrary locations with overlapping geometry and validating the resulting transforms. First, a scan matching algorithm based on a genetic search and a fractional distance metric is presented. Secondly, two metrics are proposed to verify the recovered transforms. Through experimental results the proposed algorithms are shown to robustly estimate and validate loop closure transformations for both manually and automatically defined candidates. Finally, the proposed algorithms are demonstrated in an end-to-end SLAM framework.