  We present a model-independent and relativistic approach to analytically
derive electromagnetic finite-size effects beyond the point-like approximation.
The key element is the use of electromagnetic Ward identities to constrain
vertex functions, and structure-dependence appears via physical form-factors
and their derivatives. We apply our general method to study the leading
finite-size structure-dependence in the pseudoscalar mass (at order $1/L^3$) as
well as in the leptonic decay amplitudes of pions and kaons (at order $1/L^2$).
Knowledge of the latter is essential for Standard Model precision tests in the
flavour physics sector from lattice simulations.
