This paper presents a comparative study of different existing algorithms for determining stability domains for linear systems with saturating inputs. Algorithms based on the solution of LMI problems carried out on the basis of three different saturation models, namely regions of saturation, differential inclusion, and sector modeling, are analyzed and compared in terms of their ability to provide large stability domains for the closed-loop system. The main reasons such algorithms incorporate conservativity are highlighted, this being the main contribution of this paper. Results are illustrated by means of an example.