As the World Wide Web continues to grow and change, the need to study and understand it grows. Web Science is an effort to do just this. Due to the multidisciplinary nature of Web Science, and the wide variety of data on the web it studies and produces, Web Observatories are needed to help foster collaboration and provide archiving of work and studies for future generations of researchers. In this paper, we use health data on the Web, and Health Web Science as a use case in showing how and why we need to build Web Observatories. We characterize the unique challenges that exist in building Web Observatories and present a methodology that accommodates these challenges.