The finite-difference time-domain (FDTD) method is widely used for computational electromagnetic simulations due to its efficiency and ease of implementation. However, due to its reliance on an orthogonal grid, it is difficult to represent curved and non-aligned planar surfaces. A common method of dealing with this is to use stair-cased meshes that align with the stair-cased grid as close as possible to the surface being meshed. This work explores the errors that arise from using stair-cased meshes of cavities for shielding and scattering problems. It is determined that the increased surface area of a stair-cased mesh alters the transmission and reflection of incident waves. A method of altering the boundary properties is presented to counteract the errors in transmission and reflection. This method is shown to reduce the error in the magnitude of shielding effectiveness (SE) of stair-cased cavities. However, as this method does not change the geometry of the mesh itself, errors in resonant frequency and the presence of spurious resonances is not affected. A second method is proposed to locally deform FDTD cells to conform to a curved or non-aligned planar surface. This method incorporates a thin layer model to vastly increase the efficiency of the algorithm when compared to bulk material alternatives. The method is shown to improve errors in the magnitude of SE, resonant frequency and spurious resonances when compared to stair-cased models.