You could check for biological relevance by performing enrichment analysis (e.g. Enrichr, webgestalt, gorilla, panther) on the obtained clusters.

To identify modules that may be of more relevance, after identifying them (currently under review) we recently performed enrichment analysis to see if the modules made biologic sense. In our case they did and we then went on to characterizing the networks with highest biologic relevance to our study.

There are different ways to do a network analysis. Most viable way is to do GSEA as others are suggesting to find a meaning biological modules from the given modules of WCGNA. What you can do is take each module make the GO enrichment analysis or any standard pathway analysis and then try to score the pathways based on p-value or FDR values and try to find the top pathways that are of convergent biological sense to your phenotype or experimental design. If it does then you can use any Cytoscape to create the network visualization for that module that is at the highest priority with significant p or FDR value giving you better biological relevance.