Although Network Function Virtualization (NFV) and containerized services embedded therein are an already active research field while becoming increasingly widespread in practice (e.g., 5G networks), the trust and security challenges still deserve more attention. To tackle relevant issues for this aspect, our work deals with the question of whether and how the issue of trust assessment can be addressed in such infrastructures. Different trust models are reviewed, and the trust attributes used in the literature are analysed and evaluated. These parameters are subsequently included in a trust calculation framework for their confidence analysis. Finally, a Dynamic Trust Monitoring (DTM) solution, namely MicroDTM, that supervises the trustworthiness of containerized services in an NFV infrastructure is proposed. By collecting and processing the trust parameters, a containerized service environment is evaluated according to trustworthiness for different scenarios. In addition to performance analysis, improvements and extensions necessary to use the system in a practical environment are identified.