Badly-scaled matrix pencils could reduce the reliability and accuracy of computed results for many numerical problems, including computation of eigenvalues and deflating subspaces, which are needed in many key procedures for optimal and H-infinity control, model reduction, spectral factorization, and so on. Standard balancing techniques can improve the results in many cases, but there are situations when the solution of the scaled problem is much worse than that for the unscaled problem. This paper presents a new structure-preserving balancing technique for skew-Hamiltonian/Hamiltonian matrix pencils, and illustrates its good performance in solving eigenvalue problems and algebraic Riccati equations for large sets of examples from well-known benchmark collections with difficult examples.