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.
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?