GPS has been extensively used in measurement of displacements of long, flexible bridges, but we summarize evidence that geodetic instruments, GPS (GNSS) and RTS (robotic total stations), in combination with accelerometers, can be used to measure with safety semi-static and dynamic deflections of stiff bridges with main natural frequencies> 1–3 Hz. This is possible through a methodology derived from controlled, supervised learning experiments, field evidence and structural constraints. This methodology permits to understand the noise characteristics of dynamic displacement measurements and to develop techniques to suppress their noise, and has the following characteristics:(i) it is based on redundant/collocated sensors in order to control measurement uncertainty, avoid blunders and compensate for weaknesses inherent in each type of sensor;(ii) focusses on controlled excitations with structural/logical constraints, mostly free attenuating oscillations leading to direct estimation of first modal frequencies. This methodology was applied, refined, validated and exemplified in the study of several types of bridges in Greece, covering among others, cases of progressive decay and of soil-structure interactions.