Advice on using edge weights to avoid certain edge cuts

My graphs come from 3D unstructured FE meshes (the face-adjacent cell graph) and I have certain edges that I wish to avoid being cut. (To give an indication of how these edges would be distributed in the graph, they are associated with an internal mesh surface; I'd strongly prefer the cells not be partitioned along that surface.) My thought is to put a large weight on those edges, but how large is enough to (mostly) avoid them being cut without causing problems to the partitioning algorithms. Is there some rule-of-thumb for this, and is it graph-size dependent? I'd like to avoid a per-mesh, trial-and-error approach to the partitioning process and hardwire a weight value.

Thanks again.