Measuring the apertures of the Large Hadron Collider (LHC) collimators, as well as the positions of their axes, is a challenging task. The LHC collimators are equipped with high-precision linear position sensors, the linear variable differential transformers (LVDTs). The accuracy of such sensors is limited by the peculiar parasitic effect of being rather sensitive to external magnetic fields. A new type of inductive sensor, the Ironless Inductive Position Sensor (I2PS), that keeps the advantages of the LVDTs but is insensitive to external magnetic fields has been designed, constructed, and tested at CERN. For this sensor, a detailed description of parasitic effects such as high-frequency capacitances and the presence of conductive shields and electric motor, in the surroundings is given, from analytical, numerical, and experimental viewpoints. In addition, proof is given of the I2PS's radiation hardness. The aim of this paper is to give a complete and exhaustive impact evaluation, from the metrological viewpoint, of these parasitic effects on these two fundamental sensor solutions.