How can I determine if there are π-π interactions between an amide and an aromatic ring in a protein?
It seems that NickT was looking for an experimental solution. My post deals, however, with a computational solution.


  How would I quantify how significant the interaction is?


Determining the interaction energy between two defined monomers such as your aromatic triazole and amide is a rather straightforward process.  This process is referred to as the supramolecular approach.  I'll point you to a paper that analyzes the benzene dimer.  This method is strictly a computational one so a bit of knowledge in computational chemistry is necessary.

The Supramolecular Approach

The What

The supramolecular approach boils down to this.

$$E_{\mathrm{int}} =  E_{\mathrm{dimer}} - (E_{\mathrm{mon1}} + E_{\mathrm{mon2}})$$

Here we have some interaction energy ($E_{\mathrm{int}}$) determined from the difference of a dimer energy ($E_{\mathrm{dimer}}$) and the sum of the two monomers ($E_{\mathrm{monomer}}$).  If both monomers were equivalent (say, you were interested in the interaction energy of the benzene dimer where each monomer was a benzene ring), you could simplify the summation to two times the energy of one monomer ($2\times E_{\mathrm{mon}}$). In your particular case, you have two different monomers.

The whole idea is if I have two interacting molecules, I can determine the energy of each molecule individually (as if they were separated at infinite distance) as well as their complex.  So as you bring these molecules closer and closer together, the energy starts to go down (the interaction energy).

The How

NOTE: Your geometry is from a crystal structure.  Do NOT modify this geometry.  You will want to keep everything exactly as is.  This means you don't want to optimize your system.  You do not want to eyeball monomer placement.  Take everything from your known structure and be careful not to change it otherwise it can ruin this process.  We are modifying the structure by truncating and capping but intermolecular parameters must stay the same for whatever it is you are trying to model.  You will want to optimize your cap meaning, run an optimization on your capped-monomer but freeze everything but the thing you are using to cap.


Define your monomers.  You will need to determine what part of your 'dimer' system is important for describing this weak interaction.  I recommend keeping the aromatic ring and truncating the ring with something similar to what is being truncated.  You could cap your monomer with a hydrogen or a methyl group for example.  If the piece you've cut out is highly polarizable, cap with something with a similar property.  If your truncated piece is neutral in charge, cap with something that is neutral.  You get the idea.
Define your dimer.  Your dimer is simply a combination of your two defined monomers.
Determine the method you want to implement.  Wavefunction based or density functional theory (DFT) will work for this.  The former will be prohibitively expensive. 
Define your basis set.  For aromatic systems your best bet would be to use Dunning-Hunzaga's correlation consistent family of basis sets.  I recommend using aug-cc-pVTZ for good results.  Whatever you decide, be sure your basis set includes polarization and diffuse functions.  The suggested basis set does this (augmented means diffuse on all atoms whereas pVTZ means 'polarized-valence triple zeta'). 
Determine the energies of your monomers and dimer.  You will want to run a single-point energy calculation on your monomers and your dimer. Optimize your monomers first but freeze all atoms except those you added to cap your monomer.
Determine the interaction energy.  Plug your energies into the equation given above and determine the interaction energy.  Convert to whatever units you wish to use (I prefer kJ/mol but most people use kcal/mol so you may want to use that).


I hope this helps.  Looks like an interesting project to say the least.

A quick note about the 'valence' basis set:

Typically core electrons do not participate in any sort of interesting chemistry (they are so much lower in energy than the valence electrons that they do not play a role in things like chemical bonding).  When you perform these energy computations, you will be invoking the frozen-core approximation (default on many quantum software packages but be sure to check the documentation first).  The pVTZ basis set expands the basis functions out to triple-zeta quality for valence electrons only.  The core electrons are given s-type functions and that is it.  If you ever find yourself in a situation where the core electrons are important to your system of interest, you would want to use the pCVXZ basis sets (where X = D,T,Q, etc.) which stands for polarized core-valence X zeta.  Here the core electrons are given the full set of X-zeta quality basis functions.  However this means you've just made your computation much more expensive.  The frozen-core approximation is typically used.