We report the synthesis and characterization of five new honeycomb tellurates with the PbSb2O6 structure type. These materials, SrM2/3Te4/3O6 (M = Cr, Mn, Fe) and SrM1/2Te3/2O6 (M = Co, Ni), are prepared by conventional solid state synthesis. Rietveld refinements of powder X-ray and neutron diffraction data reveal that these materials crystallize in the P (3) over bar 1m space group, in which M and Te are octahedrally coordinated and randomly distributed over the honeycomb sublattice. In three of these materials (M = Cr, Mn, Fe), the transition metal takes a 3+ oxidation state, and hence, charge neutrality necessitates that the honeycomb sublattice is 66% occupied by nonmagnetic Te. In the remaining two of these materials (M = Co, Ni), the transition metal takes a 2+ oxidation state, requiring that 75% of the honeycomb lattice is occupied by nonmagnetic Te. Thus, the honeycomb sublattice is highly diluted, as only 33% or 25% of the sites are occupied by a magnetic ion. These occupation values fall well-below the percolation threshold for the honeycomb lattice, p(c) = 70%. Accordingly, magnetic susceptibility measurements reveal no magnetic order or spin freezing down to 1.8 K.