We present a relativistic and model-independent method to derive structure-dependent electromagnetic finite-size effects. This is a systematic procedure, particularly well-suited for automatization, which works at arbitrarily high orders in the large-volume expansion. Structure-dependent coefficients appear as zero-momentum derivatives of physical form factors which can be obtained through experimental measurements or auxiliary lattice calculations. As an application we derive the electromagnetic finite-size effects on the pseudoscalar meson mass and leptonic decay amplitude, through orders O(1/L 3 ) and O(1/L 2 ), respectively. The structure dependence appears at this order through the meson charge radius and the real radiative leptonic amplitude, which are known experimentally.