An analysis of ill-posed electrodynamic problems formulated in the form of the 1-st kind Fredholm integral equations (IE) is carried out. It is shown that the Tykhonoff regularization of ill-posed problems ensures stable solutions for electromagnetic field only on the surface, where the 1-st kind Fredholm IE is posed. A well-posed method of physical regularization for electrodynamics boundary-value problems is proposed and justified.