The growing demand for solutions related to measurement (e.g., digital sensors, smart meters, distributed measuring systems) imposes several concerns about information and process reliability. In this context, blockchain can play a crucial role as a platform to implement applications and activities in the context of legal metrology. In most countries, the National Metrology Institutes (NMIs) are responsible for promoting these initiatives. Thus, in this paper, we present a functional architecture to integrate NMIs in a collaborative blockchain network. We discuss the main aspects and features that an inter-NMI blockchain network must deliver. Furthermore, we implement our proposal using the Hyperledger Fabric platform. We connect peers from Physikalisch-Technische Bundesanstalt (PTB) (German NMI) and the National Institute of Metrology, Quality, and Technology (Inmetro) (Brazilian NMI) in a useful application that consists of a blockchain-based public-key infrastructure to identify and authenticate smart meters. Our preliminary results demonstrate that the proposed architecture meets the main requirements imposed by applications involving measurements. Furthermore, it opens the opportunity to integrate NMIs from other countries into the project, constituting an important global initiative in the metrology field.