Communications systems are growing in use and in popularity. While their interactions are becoming more numerous, trust those interactions now becomes a priority. In this paper, we focus on trust management systems based on observations of trustee behaviors. Based on a formal testing methodology, we propose a formal distributed network monitoring approach to analyze the packets exchanged between the trustor, trustee and other points of observation in order to prove the trustee is acting in a trustworthy manner. Based on formal "trust properties", the monitored systems behaviors provide a verdict of trust by analyzing and testing those properties. Finally, our methodology is applied to a real industrial DNS use case scenario