We present numerical tests of five related semiclassical techniques for computing time-dependent wave functions. These methods are based on integral representations for the propagator and do not require searches for special trajectories satisfying double-ended boundary conditions. In many respects, the computational techniques involved resemble those of conventional quasiclassical treatments. Three of these methods result in globally uniform asymptotic approximations to the wave function. One such method, the treatment of Herman and Kluk, is found to be capable of especially high accuracy and rapid convergence.