After arriving at the castle, Lord Harkon gives you the option to become a vampire lord, but when I accept the offer Lord Harkon disappears. The cut scene continues though and I have the power to transform. However, I can't leave the castle without speaking to Lord Harkon. How can I find him or make him reappear?
If you're on PC, try the command
02003ba8.moveto player (assuming Dawnguard has ID 02 in your load order, which it should) to move him to you; if that doesn't work try
moveto player. If you're not playing on PC your best bet is to reload to a previous save.