Cascaded Shadow Maps is so far the best solution to tackle Perspective and Projective aliasing in shadows. The basic idea is to use multiple shadow maps (mostly 3 or 4) to cover different areas of view camera frustum. The root cause of these shadow artifacts is lack of one to one mapping between shadow map texels and pixels on the screen (in view space). The Cascaded Shadow mapping provides higher resolution shadow maps to objects closer to the eye solving the root cause of artifacts.
(Screenshot – JustAnotherGameEngine)