Make your (good) intentions clear. How can you make it easy for your clients to take the time and tie their reputation to yours?
1) Be amazing. I have a few contractors and companies that I recommend to others all the time. Why? I am 100% confident in their services. The service/product they have provided was so exceptional that they never have to ask me for a recommendation - I am doing it all the time. In fact, I think that being able to point my friends and business associates to such stellar services makes me look good. Above all - be that vendor. If you are that vendor, all you have to do is ask, and your clients will say "yes" every time. If your service has been amazing, you can ask now, if you have a little work to do, progress to step #2.
2) Invest the time to show your value. Look who your clients know, target a certain type of potential client. Outline the service/product/value for that customer type. Know how it is similar/different from what you have done for your existing client. With that information at hand call you client and ask for the introduction. By preparing for the reference you show you will be worthy of the introduction.
3) Make the introduction easy for your client. If they agree, send them an email from which they can easily extract (copy/paste) the information they will include when they introduce you to their contracts.