We prove convergence of spectra, ordered eigenvalues, eigenfunctions as well as convergence of resolvents on appropriate spaces, for traces of Dirichlet forms when the speed measure is the monotone weak limit of G-Kato measures. Some quantitative estimates are also given. As application we give an approximation procedure for the eigenvalues of the Laplacian on annular thin sets with mixed Neumann-Wentzell boundary conditions.