In this paper, we consider optimal experiment design with amplitude constraints for the case of a multisine excitation. The output amplitude constraint is robustified using an uncertainty region for the unknown true system. The main contribution of this paper is to treat the robust amplitude constraint without the classical gridding approximation. In particular, we provide an LMI optimization problem to verify whether the output constraint is respected for all systems in the uncertainty region. This LMI formulation can be combined with the accuracy constraint in the optimal experiment design problem. Like each optimal experiment design problem with amplitude constraints, the resulting optimization problem is non-convex, but we provide two approaches to efficiently initialize the algorithm used to solve this optimization problem. The efficiency of the proposed methodology is tested using a numerical simulation.