Standard methods for witnessing entanglement and steering require that some parties are able to perfectly implement a set of quantum measurements. However, real quantum devices cannot be perfectly controlled. We propose an operational framework of imprecise measurements, tailored for devices which are trusted but not flawless. We investigate how entanglement and steering witnessing is influenced by tiny systematic imperfections in the measurement devices, finding that tiny errors have large impact. Then, we set out to construct detection criteria which explicitly take the imperfections into account.