This paper will present a study on the robustness of anti-windup systems where the plant uncertainty can be expressed by LTI norm-bounded operators. The treatment is constructed under the IQC framework of Megretski and Rantzer. Robustness of anti-windup systems against LTI uncertainty using frequency dependent IQCs are less conservative than those where plant uncertainty is addressed by static IQCs. They can however increase significantly the computational burden in the algorithms. The paper shows that sufficient conditions for robustness of anti-windup systems against LTI uncertainty can be, in some circumstances, greatly simplified. They can also be expressed in the frequency domain and interpreted graphically. The test is finally exploited for anti-windup tuning.