The authors consider initial boundary value problems for Maxwell’s equations with the perfect conductor boundary condition on the smooth boundary \(\partial\Omega\) of a bounded domain \(\Omega\) driven by a self-induced current density \(J\) of the form \[ J\left(t,x\right)=-\int_{0}^{t}\sigma_{1}\left(t-s\right)\, E\left(t,x\right)\, ds \] and subject to material relations \(B\left(t,x\right)=\mu_{0}H\left(t,x\right)\), \[ D\left(t,x\right)=\varepsilon_{0}E\left(t,x\right)+\int_{0}^{t}\varepsilon_{1}\left(t-s\right)\, E\left(t,x\right)\, ds , \] \(t\in\mathbb{R}_{\geq0}\), \(x\in\Omega\), \(\varepsilon_{0},\mu_{0}\in\mathbb{R}_{>0}\). The integral kernel functions are assumed to be scalar-valued and required to satisfy \(\omega:\operatorname{Im} \widehat{\varepsilon}_{1}(\omega)- \operatorname{Re}\widehat{\sigma}_{1}(\omega)>0\) for \(\omega\in\mathbb{R}_{>0}\) to obtain long-time decay estimates for the solution. Polynomial energy decay is obtained for polynomially decaying kernel functions. The results are shown by utilizing suitable Lyapunov functionals.