Plotting Two-Dimensional Complex Waves

Is it possible to make a contour plot of a two-dimensional complex wave with the color scale representing the complex phase? Or alternatively, is there some other way to plot two-dimensional complex waves?

You can display a complex matrix as an image plot. Then you have the choice of magnitude, real part, imaginary part, or phase to be the quantity represented.

Unfortunately, contour plots accept only real waves. You would need to make a new wave with the appropriate quantity in it first.

Just a word of caution about plotting 2D phase.  Unlike 1D phase, the 2D case is a bit more complicated.  Depending on your application you may benefit from understanding the complexities of 2D phase.  I recommend looking at the documentation for ImageUnwrapPhase and references therein.