How can I safely go downhill on an antique penny-farthing bike? I recently picked up a vintage penny-farthing (high wheeler) at the flea market and, after restoration, adopted it as my normal mode of transportation.

It works well for the most part, but going downhill terrifies me as I don't want to lose control and fall from more than a meter up. 

Certainly this problem has solved before. How can I safely go downhill? Are there reliable braking systems?
Forget trying to use the brake to slow you down.  At best, the brake may shed a little speed if you're not travelling too fast, on the flat, but backward pressure on the pedals is the more effective way to lose speed (again, only really possible on the flat).  The brake will be 100% ineffective once you gather momentum and head downhill.  There is one hard and fast rule to follow:  If you can not see the bottom of the hill, or there are obstructions further down, which will require you to slow down or stop, then don't even attempt to ride down.  Dismount and push the bike downhill.

If the view forward shows the route to be clear, and you can see the bottom of the hill then it is acceptable (though not easy for a beginner) to raise your legs over the handlebars and rest them on top.  This keeps your feet out of the way of the madly spinning pedals.  You will not be able to spin your legs fast enough to keep up with the pedals, so don't try to - it will end with injury of some sort.

Ignore the advice about applying the brake gently to avoid going head-first over the handlebars.  You will never achieve this by using the brake alone.  The original spoon brakes are just not powerful enough, and certainly will not stop the wheel quickly enough to send you over the top.  "Headers" as they are known, are caused by other problems, such as the front wheel suddenly stopping because it has hit an obstacle, or become lodged in soft ground.