Protein structures are an ensemble of atoms determined experimentally mostly by X-ray crystallography or Nuclear Magnetic Resonance. Studying 3D protein structures is a key point for better understanding protein function at a molecular level. We propose a set of accurate tools, for analysing protein structures, based on the reliable method of Voronoi-Laguerre tessellations. The Voronoi Laguerre Delaunay Protein web server (VLDPws) computes the Laguerre tessellation on a whole given system first embedded in solvent. Through this fine description, VLDPws gives the following data: (i) Amino acid volumes evaluated with high precision, as confirmed by good correlations with experimental data. (ii) A novel definition of inter-residue contacts within the given protein. (iii) A measure of the residue exposure to solvent that significantly improves the standard notion of accessibility in some cases. At present, no equivalent web server is available. VLDPws provides output in two complementary forms: direct visualization of the Laguerre tessellation, mostly its polygonal molecular surfaces; files of volumes; and areas, contacts and similar data for each residue and each atom. These files are available for download for further analysis. VLDPws can be accessed at http://www.dsimb.inserm.fr/dsimb_tools/vldp.