In this work, we develop a robust method to retrieve the shape of a metallic object from partial electromagnetic measurements containing noise. The numerical resolution of the inverse problem is tackled through parametric shape optimization. To make the method robust, the expectation of the Kohn-Vogelius cost function is minimized here: the key point is to use the so-called Karhunen-Loève expansion in order to obtain an explicit deterministic shape gradient. Then, the optimization problem is solved using a Nesterov gradient scheme. Numerical tests are provided to highlight the advantages and the efficiency of the proposed method.