Study of cavities and channels in molecular structure is a crucial step in understanding the function of biomolecules. Current tools and techniques for extracting these structural features are sensitive to uncertainties in atomic position and radii. In this paper, we study the problem of cavity extraction in biomolecules while taking into account such uncertainties. We propose an approach that connects user-specified cavities by computing an optimal conduit within the region occupied by the molecule. The conduit is computed using a topological representation of the occupied and empty regions and is guaranteed to satisfy well defined geometric optimality criteria. Visualization of the set of all cavities with multiple linked views serves as a useful interface for interactive extraction of stable cavities. We demonstrate the utility of the proposed method in successfully identifying biologically significant pathways between molecular cavities using several case studies.