Sorry for the delay in follow-up (caught a bad cold right after I posted this!). I do appreciate everyone's feedback and recognize that I perhaps left out some additional details which may help shed some light on what transpired here. We landed in Zurich where we were scheduled to board KLM 1964 on the evening of Thursday, August 9th. However just prior to leaving Rome we got word that our connecting flight had been cancelled. Seeing as how we got word of this literally as we were boarding, ground staff advised us to proceed to Zurich and that staff there would assist us further.
When we arrived in Zurich, we went to KLM contracted customer service desk. Staff there said all non-stop flights to Amsterdam the next day (Friday) were fully booked. They offered us a connecting flight through Geneva on Friday but we declined since we didn't want to risk getting stranded again. Instead, they offered to put us on a non-stop flight for Saturday and gave us a two night hotel stay and a couple of meal vouchers. I'm not certain as to what the reason was for the cancellation to begin with which is why I asked if there was a way for me to find out online somewhere before filing my claim. I will try the link above though and see what they say. Thank you all for your input and assistance.