Gilbert proposed an iterative algorithm for bounding the distance between a given point and a convex set. We apply the Gilbert's algorithm with a few modifications and simplifications to get an upper bound on the Hilbert-Schmidt distance between a given state and the set of separable states. While Hilbert-Schmidt distance does not form a proper entanglement measure, it can nevertheless be used as a very robust indicator of the amount of entanglement. We provide a method based on the Gilbert's algorithm that can reliably qualify a given state as strongly entangled or practically separable, while being computationally efficient. The method also outputs successively improved approximations to the closest separable state for the given state. We show that the approximate closest separable states are useful in constructing Entanglement Witnesses (EW) that are close to optimal. We demonstrate the efficacy of the method with examples. The flexibility of the algorithm enables a study of the boundary of the sets of separable (biseparable, etc) states as well as the construction of EWs in a Hilbert space of arbitrary dimension. The above applies only in the event that the state in question is known. On the other hand, to certify non-classicality without the knowledge of the underlying shared correlations and the devices acting on those correlations we propose a simple approach to Self-Testing of Bell inequalities, which is a stricter form of Device Independent certification. Our method for Self-Testing certification requires minimal assumptions, and as we show, can be applied to a wide variety of Bell Inequalities, including quadratic Bell Inequalities, in Hilbert spaces of arbitrary dimensions.