Ultraviolet LEDs produce ultraviolet light which your eye can't see. This is how I tested to make sure that the UV LEDs I bought were working correctly.

Here's what you need:

Your UV LED
A DC Power supply or appropriate battery
Transitions glasses (Photochromatic Glass)

Step 1:

Transitions lenses use a special photochromatic coating that responds to Ultraviolet radiation. The stronger the UV radiation the darker the lenses become. I have a pair of photochromatic glasses so I used them to test out my LEDs.

Just put your glasses in front of your LEDs.
Turn the LEDs on by plugging them in.
Wait a minute or 2 with the LEDs on. It's best not to look at them without eye protection.
See if the glasses change color.

That's it!