If the capacitor plates are not ideal conductors (and have relative dietetic constant > 1), how does that change the capacitance calculations? It is my understanding that capacitance is purely related to geometry and the material BETWEEN the plates and not the plates themselves, is that correct? (The specific material I have in mind is biological tissue such as bone, muscle...)
If the conductivity of the plates in a capacitor is much better than the medium between them, then the component will look reasonably 'capacitive', albeit with some resistive losses.
Resistance in the plates will look like equivalent series resistance (ESR). Resistance in the dielectric medium will look like a parallel leakage resistance. The dielectric constant of what's between the plates will control the capacitive part of the component's impedance.
As the materials you envisage are bone and muscle, it sounds like a measurement situation. As such, you may get good results by simply sending an AC current into the capacitor and measuring the voltage. You may get better results by demodulating the voltage into components in phase with and in quadrature to the applied current to separate the capacitive and resistive components, you could increase the specificity of the measurement to the actual changes you want to track. There are one chip solutions available to do this sort of network analysis.