This paper considers the problem of balanced model reduction for a class of distributed parameter systems. The system is assumed to have a finite-dimensional state vector as well as a finite-dimensional input vector. However, the output is contained in a finite-dimensional subspace of an infinite-dimensional space. This often occurs in the modelling of physical systems such as flexible structures. acoustic ducts, etc. It is shown that a reduced model based on balanced truncation guarantees an upper bound on the H-infinity norm of the error system.