This paper discusses the resolution of geometrical characteristics of pressurized fractures from tiltmeter data. The quasi-static deformation and tilt field induced by such fractures can be modeled by superposition of displacement discontinuity (DD) singularities. Despite the relatively common use of such measurements to infer fracture characteristics, there is a widespread misunderstanding of what can be accurately determined, depending on the relative distance between the tiltmeter array and the fracture. We investigate in detail the resolution of the dimensions and orientation of hydraulic fractures or faults from tilt measurements. In particular, we formally prove that at a distance larger than about twice the characteristic length of the fracture, elastostatic measurements such as those measured by tiltmeters are not able to resolve independently all the dimensions of the fracture, although the fracture volume can be robustly inverted from the data. The resolution of fracture orientation is also discussed using an analysis based on a spatial Fourier Transform of the tilt field. The relative angle between the plane where the measurements are located and the fracture plane plays a major role in the accuracy of this estimation. In an illustrative field example, where the measurements are located in the far-field of the fracture deformation field, we show how a single DD singularity can be used to model tiltmeter data and efficiently obtain the fracture orientation and volume.