I'M NOT AN EXPERT, BUT...
Not trying to steal any thunder from anyone, but I just heard this at a HPA/SWA conference this weekend in San Antonio:
SWA is considering a separate part of the interview which is a "Leadership Scenario". The Captain who talked to us said they will have two pilots who are on the "Leadership Interview" team (separate from the Oral Interview Team).
The two pilots will give the applicant a scenario, using a paper trainer and three chairs, with the applicant in the left seat and the two interviewers in the "copilot" and "jumpseat" chairs. Simulating whatever you need, the jumpseater, the copilot, ATIS, dispatcher, ATC, etc., the two interviewers will feed you information you ask for to resolve an aircraft emergency and weather scenario.
This will be a seven-minute, timed process and they are judging how you would handle the situation from a CRM/leadership point of view. Aviation knowledge is required, but 737 specific systems knowledge won't be expected. There will also be a debrief, where you can Monday-morning quarterback yourself on how you would have done better.
The scenario and the feedback you give in the debrief will be weighed into how you did overall.
Again, I'm not an expert. I'm on the outside looking in. But, this is what we were told by a SWA Captain who is involved in the interview process. Also, he said the "Leadership" Interview will take place in the AM previous to PM interviews and PM after an AM interview.