A singly-fed circularly-polarized (CP) antenna based on coupled radiator pair with stable CP performance is proposed for the accurate positioning of smart watches in this article. It is first demonstrated that two identical coupled monopoles sharing a finite ground can be equivalent as a second-order filter network consisting of composite J/K inverters. The coupled radiators will produce a pair of even and odd modes, whose resonant frequencies and bandwidths are determined by the coupling strength. After that, characteristic mode analysis is conducted to verify the circuit model, and it reveals that the even and odd modes are orthogonal to each other, which are candidates for CP radiation. In particular, the phase difference of the two modes is determined by the coupling coefficient, and it can be elaborately manipulated by properly changing the current distribution of characteristic modes through ground size, slot-loading and radiator length. At last, two antenna prototypes are designed, implemented and measured to validate the working principle. Different from conventional CP antennas operating in degenerate modes, the proposed antennas are insensitive to perturbation segments and can maintain stable CP performance, which is highly demanded in smart watches under wearing conditions.