Reference architectures systematize and standardize the development of software systems and, hence, contribute for the reuse of design expertise on a specific domain. An adequate architectural description for reference architectures is essential for their effective use and dissemination. Nonetheless, previous studies have pointed out that the architecture description of reference architectures often presents only informal, textual descriptions, which are ambiguity prone. The main purpose of this study is to discuss directions for a precise, comprehensive description which can support the specification, analysis, and realization of reference architectures. To do so, we investigate which and how formal methods could be introduced for describing reference architectures. Considering that components can be used for realizing reference architectures, we also investigate how they could be expressed in such a formal description. In particular, we focus on embedded systems due to the sophistication required for systems in this domain. With this study, we intend to contribute to the reference architecture community with directions for promoting a formal, precise architectural description.