How to consider metal loss in moment method modeling antenna

Does it just modify the diag(Z) by adding the surface impedance of the conductor, or should be to modify the integral equation so as to consider the contribution of the equivalent magntic current?

Write down the MoM matrix equation:

V = Z * I

Then solve it:

I = Y * V

For lossless, you set all the V's to zero, except for the exictation port(s).

For lossy, set all the V's equal to the the surface resistance times the current flowing through them (Ohm's Law). There will be an extra factor too, depending on what basis function you use, just evaluate the integrals that are used in MoM.

The net effect is you modify the diagonals only except where two subsections physically overlap, in which case you modify the off diagonal elements that correspond to the overlap.