Two high-order compact-difference schemes have been developed for solving three-dimensional, time-dependent Maxwell equations. Spurious high-frequency oscillatory components of the numerical solution, which are considered to be among the principal sources of time instability, are effectively suppressed by a spatial filter. The present numerical schemes are validated by calculations of three-dimensional transient electromagnetic waves within a waveguide, an oscillating electric dipole, and the radar cross section of perfectly electrical conducting sphere.