There is a chance that you are not embeding the colour profiles on your file, and you are not working in a controled color management process. If things are running smoothly in all the process you should have a decent preview of the final look.
If you see any neon green on the exported file you have thoose settings turned off. The green is the best color to test this.
1) Work with the correct profiles in your Ilustrator program.
2) Export a medium resolution png file with the color profile embeded. (This will give you an extra saftey that the client just have a sample, not the final work for print before all the project is finished)
3) Make some tests to see if your client have some minimum quality in the monitors he is reviewing the work, but any decent browser or image viewer should read the color profile.
*The pdf file format does use this color profiles accuratley, but not all applications to read it do it well.
4) Tell your client that colors can change from monitor to monitor or device. In some next step send a printed sample in good quality.
5) If you use a pantone color that will give you a better way to confirm the color. Show the client the pantone guide too.
You have to be sure that you are seing the correct colors, but to confirm that with your client is more difficult. You should use this tools http://www.colormunki.com/ to control the first part of the process.