  We establish a method of directly measuring and estimating non-classicality -
operationally defined in terms of the distinguishability of a given state from
one with a positive Wigner function. It allows to certify non-classicality,
based on possibly much fewer measurement settings than necessary for obtaining
complete tomographic knowledge, and is at the same time equipped with a full
certificate. We find that even from measuring two conjugate variables alone,
one may infer the non-classicality of quantum mechanical modes. This method
also provides a practical tool to eventually certify such features in
mechanical degrees of freedom in opto-mechanics. The proof of the result is
based on Bochner's theorem characterizing classical and quantum characteristic
functions and on semi-definite programming. In this joint
theoretical-experimental work we present data from experimental optical Fock
state preparation, demonstrating the functioning of the approach.
