We present nuclear spectral energy distributions (SEDs) from 1 to 18 micron of a small sample of nearby, nearly face-on and undisturbed Seyfert galaxies without prominent nuclear dust lanes. These nuclear SEDs probe the central ~35 pc of the galaxies, on average, and include photometric and spectroscopic infrared (IR) data. We use these SEDs, the clumpy torus models of Nenkova et al. and a Bayesian approach to study the sensitivity of different IR wavelengths to the torus parameters. We find that high angular resolution 8-13 micron spectroscopy alone reliably constrains the number of clumps and their optical depth (N0 and tau_V). On the other hand, we need a combination of mid- and near-IR subarcsecond resolution photometry to constrain torus width and inclination, as well as the radial distribution of the clouds (sigma, i and q). For flat radial profiles (q=0,1), it is possible to constrain the extent of the mid-IR-emitting dust within the torus (Y) when N-band spectroscopy is available, in addition to near-IR photometry. Finally, by fitting different combinations of average and individual Seyfert 1 and Seyfert 2 data, we find that, in general, for undisturbed, nearly face-on Seyferts without prominent nuclear dust lanes, the minimum combination of data necessary to reliably constrain all the torus parameters is J+K+M-band photometry + N-band spectroscopy.