In this article we show that for any given Riemann surface \(\Sigma \) of genus g, we can find an upper bound for the renormalized volume of a (hyperbolic) Schottky group with boundary at infinity conformal to \(\Sigma \) . This bound depends on the genus of \(\Sigma \) and the combined extremal lengths on \(\Sigma \) of \((g-1)\) disjoint, non-homotopic, simple closed compressible curves, whose complement is the union of genus 1 components. This bound on \(\textrm{V}_{\textrm{R}}\) is used to partially answer a question posed by Maldacena about comparing renormalized volumes of Schottky and Fuchsian manifolds with the same conformal boundary.
