We study discretizations of the Maxwell-Klein-Gordon equation
as an example of a constrained geometric non-linear 
evolution partial differential equation.
For the temporal gauge we propose a fully discrete scheme which
preserves the non-linear constraint (electric charge) thanks to a special
application of Lagrange multipliers. We show that the method generalizes
 to Hamiltonian wave equations whose kinetic and potential energy 
are invariant under a group of transformations, even though the Galerkin
 spaces are not invariant.
 We then extend the method to the Lorenz gauge.
Numerical results illustrate the discussion.