Summary: High-accuracy finite-difference schemes are used to solve the two-dimensional time-domain Maxwell equations for electromagnetic wave propagation and scattering. The high-accuracy schemes consist of a seven-point spatial operator coupled with a six-stage Runge-Kutta time-marching method. Two methods are studied, one of which produces the maximum order of accuracy and one of which is optimized for propagation distances smaller than roughly 300 wavelengths. Boundary conditions are presented which preserve the accuracy of these schemes when modeling interfaces between different materials. Numerical experiments are performed which demonstrate the utility of the high-accuracy schemes in modeling waves incident on dielectric and perfect-conducting scatterers using Cartesian and curvilinear grids. The high-accuracy schemes are shown to be substantially more efficient, in both computing time and memory, than a second-order and a fourth-order method. The optimized scheme can lead to a reduction in error relative to the maximum-order scheme, with no additional expense, especially when the number of wavelengths of travel is large.