The pulsed wire method is an attractive option to measure the magnetic field in insertion devices, mainly for those with restricted access (e.g., small gaps, in-vacuum/cryogenic environments, etc.). Besides first and second field integrals, experiments have proved the feasibility of reconstructing the magnetic field profile. Undulators with a small gap and short period are — and are planned to be — used at diffraction-limited storage rings and free-electron lasers. This contribution outlines the pulsed wire system's requirements to perform magnetic field reconstruction in such undulators. We examine the main expected limitations, particularly the dispersive, finite pulse-width, discretization error, and sag effects. Furthermore, we present the current status of developing the pulsed wire system at the European XFEL.