The method of using square-integrable trial functions for representing resonant and scattering states is adapted to the generator-coordinate description of two-cluster systems. Numerical tests in an exactly soluble two-particle model indicate that the method is suitable for locating a resonance and is surprisingly accurate in predicting scattering phase shifts. The method is shown to be closely related to the Kohn variational scattering formalism used in the framework of the generator-coordinate method.