Biological complex mechanisms with oscillatory behavior are often modeled by high dimensional nonlinear ODEs systems, which makes the analysis and understanding the dynamics of the system difficult. In this work, we consider two reduced models that mimic the oscillatory dynamics of the cell cycle and the circadian clock, and study their coupling from a synthetic biology perspective. To improve the performance and robustness of the oscillatory dynamics in a living cellular environment, we consider the problem of augmenting the parameter region admitting periodic solutions. Moreover, we study the capacity for mutual period regulation and control of the coupling between the two reduced oscillators.