This paper discusses the main issues regarding the procedures for generating High Quality Data (HQD) as support for conducting realistic cyber security studies on Modern Critical Infrastructures (CI). It identifies the most important requirements of what constitutes HQD: accuracy/realism, representation, and completeness. Based on these requirements, it discusses two strategies to achieve these requirements: the data collection strategy and the data generation strategy. While in the traditional Information & Technologies Communication (ICT) sector we find a variety of freely available datasets, in CI research data sources are scarce and of limited size. On the other hand, the data generation strategy has given birth to a new body of research built on the development of simulation software and of research testbeds. The paper describes two frameworks aimed at facilitating the generation of HQD for CI security research. Experimental results including the Tennessee-Eastman chemical process and the IEEE 14-bus electricity grid demonstrate the effectiveness of the developed frameworks.