Circadian clocks are biological systems behaving as oscillators even in constant dark conditions. We propose to use a new strategy based on computational design to provide evidence on the origin and evolution of molecular clocks. We design synthetic molecular clocks having a reduced number of genes and some of them showing architectures found in nature. We analyse the response of our models under diverse forcing light-dark (LD) cycles. Our methodology allows us to evolve networks in silico using various selective pressures, which we apply to the analysis of clocks evolved to be either autonomous or phase locked. Our designed networks either have an oscillatory response with the same period as the forcing LD cycle, or they maintain their free-running period. Our methodology will allow analysing the automatic creation of a free-running period under various LD forcing functions and learning new design principles for circadian clocks.