We consider self-pulsing regimes in chains of Kerr nonlinear optical microresonators. By means of a supermodal diagonalization procedure of the conventional coupled-mode theory in time, we theoretically and numerically study the bifurcation diagrams of a singly pumped three-cavity and a doubly pumped four-cavity system: the latter allows us to predict thresholdless frequency tripling of a GHz modulation. These self-pulsing regimes are proven robust and will find applications in the generation and conversion of microwaves on an optical carrier.