In a statistical framework common paradigms for system identification are linked to parameter estimation. Due to this relation one benefits from a wide range of existing estimation procedures which are accompanied with classical results from statistics quantifying their accuracy. In applications like robust control, however, one is interested in statements quantifying the uncertainty about the unknown system in terms of its frequency response, impulse response or a variety of other system theoretic properties. These natural measures of nearness get transfigured when considering uncertainty regions in the parameter space. In our work we therefore address uncertainty quantification and the tradeoff between system complexity and variability in a coordinate-free manner. This makes it easier to measure the mismatch between estimator and true system in an application dependent manner, while allowing the usage of different parameterizations, which is a computational advantage.