Wireless pervasive computing devices are rapidly penetrating our environments, where e-Health is among the most critical ones. In the e-Health environment it is not only important to address security and privacy issues (which are usually in the focus), but also safety needs for appropriate treatment. With an increasing proportion of pervasive (smart dust) devices which lack computing power, security, privacy, and safety provisioning in such environments is a demanding task - not to mention additional requirement about their adaptive provisioning. However, some twenty years ago an interesting research branch in computing domain appeared, called trust management. This branch is considered as a very handy alternative to support traditional hard security and privacy approaches. It is, therefore, often referred to as soft security (privacy) provisioning mechanism. As trust is inherently adaptive and as security and safety are much related, this paper presents a new approach where trust management is deployed in e-Health environments to enable adaptive safety provisioning. This paper also introduces a trustworthiness calculation framework that extends trust management methods with a comparative analysis of computational trust in Internet of Things (IoT).