I’d set up a Virtualbox VM as a portable “surfing machine” with which I can connect to my OpenVPN server. However, once I’d initiated a connection with the server, I wasn’t able to browse anywhere. A bit of Google-fu showed that apparently Ubuntu 16.04 loses DNS after connecting with OpenVPN, and by adding nameserver 8.8.8.8 (or pick your favorite DNS server) to /etc/resolvconf/resolv.conf.d/head solves this issue.
Link for future reference: https://ubuntuforums.org/showthread.php?t=2352821