Digitalization and the rapid development of IoT systems has posed challenges for metrology because it has been comparatively slow in adapting to the new demands. That is why the digital transformation of metrology has become a key research and development topic all over the world including the development of machine-readable formats for digital SI (D-SI) and digital calibration certificates (DCCs). In this paper, we present a method for using these digital formats for metrological data to enhance the trustworthiness of data and propose how to use digital signatures and distributed ledger technology (DLT) alongside DCCs and D-SI to ensure integrity, authenticity, and non-repudiation of measurement data and DCCs. The implementation of these technologies in industrial applications is demonstrated with a use case of data exchange in a smart overhead crane. The presented system was tested and validated in providing security against data tampering attacks.