We study the evolvability and dynamics of artificial genetic regulatory networks (GRNs), as active control systems, realizing simple models of biological clocks that have evolved to respond to periodic environmental stimuli of various kinds with appropriate periodic behaviors. GRN models may differ in the evolvability of expressive regulatory dynamics. A new class of artificial GRNs with an evolvable number of complex cis-regulatory control sites—each involving a finite number of inhibitory and activatory binding factors—is introduced, allowing realization of complex regulatory logic. Previous work on biological clocks in nature has noted the capacity of clocks to oscillate in the absence of environmental stimuli, putting forth several candidate explanations for their observed behavior, related to anticipation of environmental conditions, compartmentation of activities in time, and robustness to perturbations of various kinds or to unselected accidents of neutral selection. Several of these hypotheses are explored by evolving GRNs with and without (Gaussian) noise and blackout periods for environmental stimulation. Robustness to certain types of perturbation appears to account for some, but not all, dynamical properties of the evolved networks. Unselected abilities, also observed for biological clocks, include the capacity to adapt to change in wavelength of environmental stimulus and to clock resetting.