  We develop a systematic approach to determine and measure numerically the
geometry of generic quantum or "fuzzy" geometries realized by a set of
finite-dimensional hermitian matrices. The method is designed to recover the
semi-classical limit of quantized symplectic spaces embedded in $\mathbb{R}^d$
including the well-known examples of fuzzy spaces, but it applies much more
generally. The central tool is provided by quasi-coherent states, which are
defined as ground states of Laplace- or Dirac operators corresponding to
localized point branes in target space. The displacement energy of these
quasi-coherent states is used to extract the local dimension and tangent space
of the semi-classical geometry, and provides a measure for the quality and
self-consistency of the semi-classical approximation. The method is discussed
and tested with various examples, and implemented in an open-source Mathematica
package.
