We consider an initial boundary value problem for Maxwell's equations in the space-time cylinder generated by the time interval [0, T]. For this hyperbolic type system, we derive guaranteed and computable upper bounds of the difference between the exact solution and any pair of vector fields that belongs to the natural admissible energy class. Our analysis is based upon transformations of the canonical integral relation and Gronwall's inequality and generalizes the method suggested in [22] for the wave equation to the case of the Maxwell's equation.