mower won't start?

while mowing last, a couple of times the mower cut out (almost died) while mowing but then would re-start in a sense and one time quit completely but re-started immediately. Then when i shut off to go to backyard, the mower would only click-click when trying to start (clicks seemed to be coming from starter). I tightened the battery connections to no avail. I metered the battery at cables just off battery terminals and got 12+ volts so assumed good connection there. I pulled the starter/solenoid, but wondering if there is a way to check starter/solenoid for problems before reinstalling? Mower is a JD hydro 185. Thanks for any help!!!