By increasing the mesh density theoretically you could get increasingly better results. However, (depending on the method as well) when mesh cell-size gets smaller and smaller, the discretization error gets smaller (since the geometry is modelled better) but a roundoff error starts to appear since the algorithm has to deal with even smaller field values between adjacent mesh cells...
Very interesting paper about this matter (attached):
Computation of Electromagnetic Fields
Wexler A.
IEEE Trans. on Microwave Theory and Techniques, Vol. MTT-17, No.8, August 1969
Moreover, according to Chew, Jin, Michielssen and Song, “Fast and efficient algorithms in computational electromagnetics” (Artech House, 2001), when solving Maxwell equations in differential form in a discrete mesh, the computational code introduces a small phase-velocity error into the calculated field. This error is cumulating when the mesh cell gets even smaller.. In contrast, when solving the integral form of Maxwell equations, the field is computed by a Green integral function in a closed-form and thus, the cumulative error is smaller..
mogwai.