I ended up entering the url being requested in Chrome. On the left side of the address there is a lock indicating the presence of a secure site. I clicked on it and chose to view certificate information. Under the details tab I was able to copy the certificate to a file. I chose the bottom (most specific certificate) to export and chose the default export options.
Next I found a lot of online discussion about a keystore. Disliking command line options, especially when it comes to long paths and debugging I found an application that seems to work well: http://portecle.sourceforge.net/
Of note, I also tried the Java window in the control panel (Windows 7) and this didn't work for me. I am guessing this is because it is tied to the main JRE on my computer, not the Mathworks JRE.
Apparently, for maximum awesomeness, Matlab ships with its own JRE, except for Macs where it uses the system's JRE. This seems like a bad design decision to me ... See: http://www.mathworks.com/support/solutions/en/data/1-1812J/
Specifically, I think you need to update the cacerts file of the jre, which for me was located at: $Matlab/sys/java/jre/win64/jre/lib/security/cacerts
Using Portecle I opened this file and added the exported certificate. After importing I believe it also gave me a chain error (presumably since I hadn't exported the other certificates), but Portecle asked me if I wanted to trust it anyway, to which I replied yes.
Anyway, I really dislike any solution that requires me to do anything with the installation and operating system instead of from a function directly in Matlab. Any better solution?