Fly nonstop from Fort Lauderdale to Grand Cayman for $192 roundtrip on Southwest Airlines.
Flights are available for travel Monday through Thursdays from late-August through mid-December.
As with all Southwest flights, tickets can only be purchased with Southwest directly over the phone or on southwest.com. Seen below, I found seats departing FLL on Thursday, September 27 and returning from GCM on Monday, October 1, 2018. If you're interested in this fare, you'll have until midnight tomorrow, August 2nd to book.
Fort Lauderdale has a lot of flight deals on sale from Southwest, so make sure to have a look at the FLL flight deal page here for a full listing.
Need a room in Grand Cayman? Here's a list of beachside hotels for the sample dates on Hotelwatchdog.