The complexities of X-ray crystallography and NMR spectroscopy for large protein complexes, and the comparative ease of approaches such as electron microscopy mean that low-resolution structures are often available long before their atomic resolution equivalents. To help bridge this gap in knowledge, we present 3SOM: an approach for finding the best fit of atomic resolution structures into lower-resolution density maps through surface overlap maximization. High-resolution templates (i.e. partial structures or models for multi-subunit complexes) and targets (lower-resolution maps) are initially represented as iso-surfaces. The latter are used first in a fast search for transformations that superimpose a significant portion of the target surface onto the template surface, which is quantified as surface overlap. The vast search space is reduced by considering key vectors that capture local surface information. The set of transformations with the highest surface overlap scores are then re-ranked by using more sophisticated scores including cross-correlation. We give a number of examples to illustrate the efficiency of the method and its restrictions. For targets for which partial complexes are available, the speed and performance of the method make it an attractive complement to existing methods, as many different hypotheses can be tested quickly on a single processor.