Seems through some sort of array, you'll need to identify a specific miRNA you are looking for. If you have specific miRNA targets, then as del Mazo mentioned, primer design or taqman probes could be used. Careful with the primer design as you'll need to distinguish between pri-miRs, pre-miRs, and the mature active miR you're investigating.
Yea, we can first decide which proteins we are studying. The do in silico search for corresponding miRNA. Then see the expression of those miRNAs specifically. Stem loop method helps great deal.
I do agree with Jesus del Marzo. You will require specific TaqMan probes and stem loops primers, I have used the ones from A§B, they are very specific and work pretty well.