Time-resolved diagnostics are fundamental for x-ray free-electron lasers (FELs). Radio-frequency (RF) transverse deflector structures (TDSs) are typically employed to characterize the temporal properties of the electron beams driving FELs. In this article, we present time-resolved measurements with a resolution below one femtosecond using a C-band RF TDS at SwissFEL, the x-ray FEL facility at the Paul Scherrer Institute in Switzerland. The sub-femtosecond resolution is partially achieved due to an optimized optics setup and fits the expected values, showing a good understanding of our models. Measurements with a sub-femtosecond resolution are of crucial importance for ultra-fast x-ray FEL applications.