The paper deals with a class of block three-by-three saddle-point problems which appear when finite element methods are used to solve time-dependent Maxwell equations with discontinuous coefficients. Even though the considered block three-by-three linear system can be seen as a special case of the classical saddle-point problem, well known numerical methods cannot be used directly. Indeed, the considered linear system needs numerical methods based on its specific structure. Therefore the authors extend the Uzawa method, already presented in literature. Such extension requires the exact solution of a symmetric indefinite system of linear equations at each step. To avoid heavy computations at each step, an inexact Uzawa method is proposed. Theoretical analysis is provided to show that the inexact Uzawa method converges to the unique solution of the considered linear system under suitable assumptions. Four algorithms are presented and studied in details and then compared. Their performance is tested and significant numerical examples are reported to enlighten the features of the presented approach. Remarkably, numerical results also show that the inexact Uzawa method is more effective that the MINRES method.