Suppose a cubic waveguide, made of perfect conductor, has only two open parallel sides. And the boundary conditions in this case are that the electric field at the surface must satisfy:
$$\vec{B} \cdot \vec{n}=0,$$
and magnetic field:
$$\vec{E} \times \vec{n}=0,$$
where the $\vec{n}$ is the normal vector pointing outwards from the conductor. These two relations come from the equations:
$$\nabla \cdot \vec{B}=0,$$ $$\nabla \times \vec{E}=0.$$
The question is how to derive the other boundary condition that at the surface the electric field must satisfy:
$$\frac{\partial{E_n}}{\partial n}=0.$$
$E_n$ means the electric field along normal direction.