Boundary element discretizations of exterior Maxwell problems lead to dense complex non-Hermitian systems of linear equations that are difficult to solve from a linear algebra point of view. We show that the recently developed class of inverse-based multilevel incomplete LU factorization has very good potential to precondition these systems effectively. This family of algorithms can produce numerically stable factorizations and exploits efficiently the possible symmetry of the underlying integral formulation. The results are highlighted by calculating the radar-cross-section of a full aircraft, and by a numerical comparison against other standard preconditioners.