Circular polarization is an essential feature for small antennas designed to connect with satellite navigation systems. Here, a Q-factor optimization problem constrained with a circular polarization radiation requirement is formulated and solved. The constrained problem is shown to be solvable as fast as calculating the Q-factor bound without the constraint. Two antenna models are designed to assess the bounds. One aims for bandwidth, and the other for circular polarisation. The well-known relation between the Q-factor and the available bandwidth is used to evaluate the designs. The circularly polarised antenna is close to the bound and has a wide field of view. The Q-factor bound provides insight into desirable antenna positions on the small device.