Define conventional? The presence of an unpaired electron and its chemical properties in relation to a SOMO model can be clearly obtained with EPR. If really only a check of the presence of a unpaired electron is desired, a SQUID could suffice. If you want to use an optical technique, and assuming you are dealing with a transition metal complex, you'd have to find a method to take advantage of spin-orbit coupling effects, but that would depend on the particular electronic structure of what you are trying to study.

Thanks, Ivan G Pallares ! I want to figure out SOMO formation through UV absorption or fluorescence spectroscopy based approach apart of EPR or SQUID.

NP! The only thing I can think of if somehow you can take advantage of the triplet state to modulate the fluorescence intensity. Maybe you can add a radical quencher like TEMPO to modulate the intensity of your compound, maybe even get some band shifts. Reasoning is if a stable complex forms, you're spectrum would pick those changes up. Long shot but that's what I would try if I had no other choice.