The interesting physicochemical characteristics of nanomaterials (NMs) has brought about their increasing use and, consequently, their increasing presence in the environment. As emergent contaminants, there is an urgent need for new data about their potential side-effects on human health. Among their potential effects, the potential for DNA damage is of paramount relevance. Thus, in the context of the EU project NANoREG, the establishment of common robust protocols for detecting genotoxicity of NMs became an important aim. One of the developed protocols refers to the use of the comet assay, as a tool to detect the induction of DNA strand breaks. In this study, eight different NMs—TiO2NP (2), SiO2NP (2), ZnONP, CeO2NP, AgNP, and multi-walled carbon nanotubes (MWCNT)—were tested using two different human lung epithelial cell lines (A549 and BEAS-2B). The comet assay was carried out with and without the use of the formamidopyrimidine glycosylase (FPG) enzyme to detect the induction of oxidatively damaged DNA bases. As a high throughput approach, we have used GelBond films (GBF) instead of glass slides, allowing the fitting of 48 microgels on the same GBF. The results confirmed the suitability of the comet assay as a powerful tool to detect the genotoxic potential of NMs. Specifically, our results indicate that most of the selected nanomaterials showed mild to significant genotoxic effects, at least in the A549 cell line, reflecting the relevance of the cell line used to determine the genotoxic ability of a defined NM.