Polymers undergo severe low-dimensionality effects when they are confined to ultrathin films since most of the structural and dynamical processes involving polymer molecules are correlated to length scales of the order of nanometers. However, the real influence of the size limitation over such processes is often hard to identify as it is masked by interfacial effects. We present the fabrication of a new type of nanostructure consisting of poly[[9-(1-octylnonyl)-9H-carbazole-2,7-diyl]-2,5-thiophenediyl-2,1,3-benzothiadiazole-4,7-diyl-2,5-thiophenediyl] (PCDTBT) thin film that is held up exclusively over tips of poly(ether-ether-ketone) (PEEK) nanopillars. The fabrication method exploits the nonwetting behavior of PCDTBT onto an ordered PEEK nanopillar array when the mobility of the PCDTBT molecules is enhanced by a solvent annealing process. We use this new configuration to characterize the mechanical behavior of free-standing thin film regions, thus in the absence of underlaying substrate, by means of an atomic force microscope (AFM) setup. First, we study how the finite thickness and/or the presence of the underlying substrate influences the mechanical modulus of the material in the linear elastic regime. Moreover, we analyze deep indentations up to the rupture of the thin film, which allow for the measurement of important mechanical features of the nanoconfined polymer, such as its yield strain, the rupture strain, the bending rigidity, etc., which are impossible to investigate in thin films deposited on substrates.