Mapping software is difficult to test because it is very costly to evaluate its output. This difficulty is generally known as the oracle problem, a fundamental challenge in software testing. In this paper, we propose a metamorphic testing strategy to alleviate the oracle problem in testing mapping software. We first conduct a case study to test Google Maps, the most popular web mapping service. The results of the case study show that our testing approach is effective, with the detection of several real-life bugs that can hardly be exposed under conventional testing paradigms. Following this, we conduct an analysis of the system OpenStreetMap, well-known open-source mapping software built and maintained by a community of users. We show the potential of metamorphic testing for such systems. These case studies show that metamorphic testing can be applied to mapping software for both verification and validation purposes.