The design of anti-windup schemes for fractional-order PID controllers is addressed in this paper. The use of techniques typically employed for integer-order PID controllers is discussed and compared for fractional-order ones, showing that the back-calculation method is the one that provides in general the best performance. Further, a new scheme that involves the use of the (fractional) derivative action is proposed. In particular, the derivative action switches between two different values when the control variable saturates in order to reduce the saturation effects as much as possible. Simulation results are presented in order to demonstrate the effectiveness of the approach.