Based on the experience of having lived through the past seven years, I think I can boil down to five the questions I consider important in trying to assess a presidential candidate's moral grounding. Sure, these overlap with broad religious principles, but they work from a secular standpoint, as well.
First, are you able to admit a mistake and, as a chief executive, take responsibility for it and work humbly to undo any damage resulting from it?
Second, will you listen to others and give thoughtful weight to reasonable arguments with which you may be inclined to disagree?
Third, will you show sufficient curiosity about the world to believe that you can learn from and respond with care to changing global circumstances that affect your fellow citizens?
Fourth, will you demonstrate enough respect to other human beings to be truthful with them, even if that costs you politically?
And finally, will you state categorically that you will not start a war?