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Integration of high permittivity dielectrics or commonly named high-k dielectrics is widely investigated as a way to reduce passive component size in the chip. The complex permittivity microwave characterisation of medium-k materials such as HfO2 and high-k materials such as SrTiO3 is presented. The characterisation method, using coplanar, microstrip waveguides or metal-insulator-metal (MIM) capacitor, allows a large band characterisation, from 40-MHz to 40-GHz. It also allows investigating these materials with a large-scale thickness, from 10 up to 500-nm, in different technological configurations, appropriate for insulators from immature to mature, that is, those which are ready for the integration in an advanced damascene architecture of MIM capacitor. It is shown that the permittivity of such materials can be process- and frequency-dependent.