Nuclear magnetic resonance (NMR) portable devices are now being used for nondestructive in situ analysis of water content, pore space structure and protective treatment performance in porous media in the field of cultural heritage. It is a standard procedure to invert T(1) and T(2) relaxation data of fully water-saturated samples to get "pore size" distributions, but the use of T(2) requires great caution. It is well known that dephasing effects due to water molecule diffusion in a magnetic field gradient can affect transverse relaxation data, even if the smallest experimentally available half echo time tau is used in Carr-Purcell-Meiboom-Gill experiments. When a portable single-sided NMR apparatus is used, large field gradients due to the instrument, at the scale of the sample, are thought to be the dominant dephasing cause. In this paper, T(1) and T(2) (at different tau values) distributions were measured in natural (Lecce stone) and artificial (brick samples coming from the Greek-Roman Theatre of Taormina) porous media of interest for cultural heritage by a standard laboratory instrument and a portable device. While T(1) distributions do not show any appreciable effect from inhomogeneous fields, T(2) distributions can show strong effects, and a procedure is presented based on the dependence of 1/T(2) on tau to separate pore-scale gradient effects from sample-scale gradient effects. Unexpectedly, the gradient at the pore scale can be, in some cases, strong enough to make negligible the effects of gradients at the sample scale of the single-sided device.