A growing need for developing new multi-functional materials operating at microwave frequencies is demanding a better understanding of ferroelectric and ferrimagnetic materials and their combinations. Some of these materials exhibit tunable physical properties, giving an extra degree of freedom in the device design. New multifunctional ferroelectric and ferrimagnetic thin film structures are investigated in this dissertation research, in which dielectric and magnetic properties can separately be tuned over a certain frequency range. The materials of choice, Ba0.5Sr0.5TiO3 (BST) and BaFe12O19 (BaM), both well studied and used in many microwave applications, were prepared using rf magnetron sputtering and pulsed laser ablation. Thin-film bilayers, multilayers and composite thin films were grown on various substrates, and their underlying microstructure and crystallographic properties were analyzed and optimized. After identifying the most successful growth conditions,dielectric and magnetic properties were measured. Unusual features in magnetic hysteresis loops in both sputtered and laser ablated films grown under different conditions were observed. Microcircuits were fabricated using optical lithography and microwave properties and tunability were tested in the range 1-65 GHz.