We have conceived and built the HILITE (High-Intensity Laser-Ion Trap Experiment) Penning-trap setup for the production, confinement and preparation of pure ensembles of highly charged ions in a defined quantum state as a target for various high-intensity lasers. This enables a broad suite of laser-ion interaction studies at high photon energies and/or intensities, such as non-linear photo-ionisation studies. The setup has now been used to perform experiments at one such laser facility, namely the FLASH Free-Electron Laser at DESY in Hamburg, Germany. We describe the experimental possibilities of the apparatus, the results of the first measurements and future experiments at other laser facilities.