In this paper we present a method for the multi-resolution comparison of biomolecular electrostatic potentials without the need for global structural alignment of the biomolecules. The underlying computational geometry algorithm uses multi-resolution attributed contour trees (MACTs) to compare the topological features of volumetric scalar fields. We apply the MACTs to compute electrostatic similarity metrics for a large set of protein chains with varying degrees of sequence, structure, and function similarity. For calibration, we also compute similarity metrics for these chains by a more traditional approach based upon 3D structural alignment and analysis of Carbo similarity indices. Moreover, because the MACT approach does not rely upon pairwise structural alignment, its accuracy and efficiency promises to perform well on future large-scale classification efforts across groups of structurally-diverse proteins. The MACT method discriminates between protein chains at a level comparable to the Carbo similarity index method; i.e., it is able to accurately cluster proteins into functionally-relevant groups which demonstrate strong dependence on ligand binding sites. The results of the analyses are available from the linked web databases http://ccvweb.cres.utexas.edu/MolSignature/ and http://agave.wustl.edu/similarity/. The MACT analysis tools are available as part of the public domain library of the Topological Analysis and Quantitative Tools (TAQT) from the Center of Computational Visualization, at the University of Texas at Austin (http://ccvweb.csres.utexas.edu/software). The Carbo software is available for download with the open-source APBS software package at http://apbs.sf.net/.