Focusing on upcoming challenges in lightweight design, such as increasing emission targets or novel multimaterial connections, versatile applicable and environmentally friendly production technologies are crucial. In this context, mechanical joining technology clinching offers a fast and energy-efficient procedure for assembling sheet metals, being a proper alternative to established joining methods, such as spot welding. However, the design of clinch points is a challenge, which is partly supported by numerical or data-based approaches for optimal tool dimensions assuring proper joint characteristics. While this is usually done for an ideal environment, real joining processes are characterized by multiple inevitably varying parameters, e.g. of the material, which have a significant impact on the quality of clinch points. Therefore, this contribution addresses the current gap by analyzing the effect of parameter variations or uncertainties on the resulting joint characteristics and studying the impact of the nominal tool design. Thus, an efficient meta-model-based variation simulation procedure is proposed and used for analyzing the effect of different tool design configurations and variation scenarios. Based on the results, it was found that varying process parameters have a strong impact on the resulting joint characteristics, whereby the effect significantly depends on the nominal tool design. This reveals the potential for a robust tool design and implies that the nominal tool design and the tolerancing of parameters should be done simultaneously for a reliable virtual joining point design without extensive iterations and physical tests.