Nanomedicines are a novel class of therapeutics that benefit from the nano dimensions of the drug carrier. These nanosystems are highly advantageous mainly within cancer treatment due to their enhanced tumor accumulation. Monolayer tumor cells frequently used in routine preclinical assessment of nanotherapeutics do not have a spatial structural architecture that allows the investigation of the penetration of nanomedicines to predict their behavior in real tumor tissue. Therefore, tumor spheroids from colon carcinoma C26 cells and glioblastoma U87-MG cells were used as 3D in vitro models to analyze the effect of the inner structure, hydrodynamic size, dispersity, and biodegradability of N-(2-hydroxypropyl)methacrylamide (HPMA) copolymer-based nanomedicines carrying anticancer drug pirarubicin (THP) on the penetration within spheroids. While almost identical penetration through spheroids of linear and star-like copolymers and also their conjugates with THP was observed, THP penetration after nanomedicines application was considerably deeper than for the free THP, thus proving the benefit of polymer carriers. The cytotoxicity of THP-polymer nanomedicines against tumor cell spheroids was almost identical as for the free THP, whereas the 2D cell cytotoxicity of these nanomedicines is usually lower. The nanomedicines thus proved the enhanced efficacy within the more realistic 3D tumor cell spheroid system.