Trustworthiness is a moral value considered to be a virtue. A trustworthy person is someone in whom you can place your trust and rest assured that the trust shall not be betrayed. A person can prove their trustworthiness by fulfilling an assigned responsibility - and as an extension of that, not to let down expectations. The responsibility can be either material, such as delivering a mail package on time, or it can be non-material such as keeping an important secret to themselves. A trustworthy person is someone that you can tell your worries and secrets to and know they won't repeat them without your permission. In general, in order for trust to be earned, worth and integrity must be proven over time.
A trusted component has a set of properties that are relied upon by another component. If A trusts B, this means that a violation in those properties of B might compromise the correct operation of A. Observe that those properties of B trusted by A might not correspond quantitatively or qualitatively to B’s actual properties. This happens when the relation is not taken into account by the designer. In consequence,trust should be placed to the extent of the component’s trustworthiness. The trustworthiness of a component is thus, not surprisingly, defined by how well it secures a set of functional and non-functional properties, deriving from its architecture, construction, and environment, and evaluated as appropriate.
See also 
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- Paulo Verissimo, Miguel Correia, Nuno F. Neves, Paulo Sousa.Intrusion-Resilient Middleware Design and Validation. In Annals of Emerging Research in Information Assurance, Security and Privacy Services, H. Raghav Rao and Shambhu Upadhyaya (eds.),Elsevier, to appear. 2008.