You have three possibilities, not counting replacing the fixture and or striking out. I've been dealing with lighting manufactures for over 25 years and it is surprising how little information they put on their fixtures. It's probably that way to keep out of lawsuits in case of something failing.
- Take a matching shade to a lighting store and see if they have it. If not consider replacing all the shades with one that they stock. The good thing about it is that if another breaks you know where to get a replacement.
- Turn off the breaker (not just the light switch) take the fixture off the wall or ceiling and look for a sticker on it with the manufactures name on it. This will get you pointed to the correct web site that you can find the fixture part number. There might be a contact number for the country you are in and you can call them find a replacement.
- Here's the Sherlock Holmes version and the last resort. Turn off the breaker (not just the light switch) take the fixture off the wall or ceiling and find the UL sticker for it. When you find that look for a number that has an 'e' in front of it like e223973. Now go the UL Online Certifications Directory Enter the UL number and it should give you the manufacturer. Hopefully the stars will be aligned and you will find everything you need.
If you are lucky like me and live in a track house, remember the electrical went to the lowest bidder and cheap fixtures and manufacturers come and go.
The third sounds the most fun, but the 1st is the most practical and you can have a new fixture just by changing the shades. Getting shades shipped is hit or miss on getting it not broken, and postal, UPS or Fedex or ??? does not insure glass. Also if you do find it on the internet, there is always the possibility that the design or neck has been modernized and will not match or fit what you have.