This paper proposes two different path following control schemes for a stratospheric airship with actuator saturation. Each of the control schemes consists of a guidance loop and an attitude control loop. In both schemes, guidance laws are designed according to the line-of-sight guidance-based path following principle. In the first control scheme, a robust H controller without constraints is designed based on the planar model of a stratospheric airship to stabilize path-following errors. The input constraints are then addressed by using a regional L2-based model recovery anti-windup compensator, which prevents the unconstrained controller from misbehaving in the constrained closed loop with anti-windup augmentation and ensures the systematic stability. In the second control scheme, model predictive control is applied to guarantee the path-following of the closed-loop system and explicitly address the magnitude and rate of rudders of the stratospheric airship. Theoretical results are illustrated by numerical simulations where both closed-loop systems are capable of following their desired paths and the constraints on control inputs are satisfied.