Understanding cell responses to the topography they are interacting with has a key role in designing surfaces due to the distinctiveness in the responses of different cell types. Thus far, a variety of surface textures have been fabricated, and the cellular responses of diversified cell lines to the surface textures have been assessed together with surface chemistry. However, the results reported in the literature are contradictory, and also not in-depth for inferring the relevance between cells, surface chemistry, and surface topography. Starting from this point of view, we focused on fabricating surfaces having extracellular matrix-like surface patterns and investigated the influence of patterning on human ovarian cancer cells. In this study, hemispherical protrusion-shaped, nanotextured surfaces were prepared via colloidal lithography and polymer casting methods using monolayer templates prepared from 280 nm, 210 nm, and 99 nm polystyrene particles and polydimethylsiloxane moulds. Then, the surface textures were transferred to biocompatible polycaprolactone films. After the characterisation of the surfaces via atomic force microscopy, X-ray photoelectron spectroscopy, and contact angle measurements, the cellular response to topography was evaluated by cell attachment, viability, and apoptosis studies. The results were compared with non-textured surfaces and control plate wells. The results showed that human ovarian cancer cell attachment increased with nanotexturing, which suggests that nanotexturing may be a promising approach for cancer cell modulation, and may have the potential to introduce new strategies for cancer treatment.