You can determine the effect of deuteration on amide 15N relaxation rates by measuring T1 and T2 using standard pulse sequences in the Varian or Bruker pulse sequence libraries. Simply make the measurements using protonated protein and fit values for T1 and T2 using any standard curve fitting software. Then repeat the measurements using your randomly deuterated protein and compare the fitted T1 and T2 values for the deuterated and protonated protein samples. T2 should show a noticeable increase, especially as the deuteration percentage gets higher than approximately 60%. Proton relaxation experiments are trickier because the relaxation rates are affected noticeably by coupling to remote non-bonded protons in addition to the usual effects from the coupling to the directly bonded 15N or 13C nucleus.

Perhaps we could offer more specific comments if you would go into a little more detail about what exactly you want to determine and how exactly you want to use the information.