It has been long thought that microscopic mechanisms related to magnetic short-range order were responsible for the temperature dependence of the electron paramagnetic resonance g tensor in low-dimensional magnetic systems. We show here that the demagnetizing field can explain qualitatively and quantitatively the observed features, i.e., ͑i͒ the g shift, variation of the g value, ͑ii͒ the presence of magic angles where there is no g shift, and ͑iii͒ the reorientation of the g tensor with temperature. These features are discussed theoretically and supported experimentally in purely organic insulating compounds. Previous results obtained on two different nitroxide derivatives are revisited in this framework. The role of the demagnetizing field may probably be generalized to most low-dimensional molecular materials.