The ability to characterize static and time-dependent electric fields in situ is an important prerequisite for quantum-optics experiments with atoms close to surfaces. Especially in experiments which aim at coupling Rydberg atoms to the near field of superconducting circuits, the identification and subsequent elimination of sources of stray fields is crucial. We present a technique that allows the determination of stray-electric-field distributions (F str x ( r), F str y ( r), F str z ( r)) at distances of less than 2 mm from (cryogenic) surfaces using coherent Rydberg-Stark spectroscopy in a pulsed supersonic beam of metastable 1s 1 2s 1 1 S0 helium atoms. We demonstrate the capabilities of this technique by characterizing the electric stray field emanating from a structured superconducting surface. Exploiting coherent population transfer with microwave radiation from a coplanar waveguide, the same technique allows the characterization of the microwave-field distribution above the surface.Hybrid systems aiming at coupling the internal state of atoms to solid-state devices have attracted significant interest in recent years. Realizations of such systems include neutral atoms close to atom chips [1][2][3][4][5][6][7][8], tapered fibers [9,10] or photonic waveguides [11,12], Rydberg atoms close to mesoscopic devices [13][14][15] and ions near surfaces [16,17]. An important motivation for the development of hybrid systems is the combination of the long coherence times characteristic of atomic ensembles and the strong interactions and fast processing capabilities of solid-state devices as a route towards scalable quantum computing [14,15,18]. Atomic and solid-state systems can be coupled by electromagnetic fields which have to be controlled with high accuracy. For example, in our experiment we aim at realizing strong coupling between Rydberg atoms and solid-state circuit QED devices [19,20] using microwave fields. Stray fields emanating from the patterned surfaces of solid-state devices in general are of major concern in hybrid systems involving ions [16,17] and Rydberg atoms [13][14][15]. The sources of stray fields are manifold and include surface adsorbates [21][22][23], polycristalline surface patches [24], and charges in the isolating gaps of coplanar waveguides (CPW) [25]. Although detrimental effects of electric stray fields might be mitigated in some cases, e.g., by microwave frequency dressing [26], coating the surfaces with adsorbates [27] or choosing chemically inert atoms (such as helium) [28,29], techniques to measure stray fields are essential. A possible technique in this context is based on Rydberg-electromagnetically-induced transparency, with which also the microwave field in a glass cell [30] or of a coplanar waveguide (CPW) [31,32] has been characterized.In this article, we present a technique to measure static and time-dependent (microwave) electric fields above patterned surfaces in a cryogenic environment based on coherent Rydberg-Stark spectroscopy. We use a fast (v ≈ 1700 m/s) supersonic bea...