We propose convenient inferential methods for potentially nonstationary multivariate unobserved components models with fractional integration and cointegration. Based on finite-order ARMA approximations in the state space representation, maximum likelihood estimation can make use of the EM algorithm and related techniques. The approximation outperforms the frequently used autoregressive or moving average truncation, both in terms of computational costs and with respect to approximation quality. Monte Carlo simulations reveal good estimation properties of the proposed methods for processes of different complexity and dimension.