When you meet a new client for the first time, do you do any follow up with them after the meeting? It is common courtesy to send off a quick email (at the least) to say that it was nice to meet the person. Try to add a special detail from your conversation that shows you aren't just sending a form letter.
Here's an example of a short and sweet follow-up letter you could send:
After so many emails back and forth, it was great to finally meet you today. I enjoyed hearing about your company and what you do, and look forward to working with you in the near future.
I hope your children feel better soon. It must be awful when both are sick at the same time!
All the best
The key is to simply be yourself. Don't think that you need to use impressive language or show off a huge vocabulary. Be as sincere as you (hopefully) were at the meeting.
Try to send your "great to meet you" mail as soon as possible. I try to send it as soon as I get back to the office (or home) from the meeting. Then when they get back and check their mail, my note will be there waiting for them. It makes a fabulous impression, shows that you care about the person and that you hope to build a relationship with him or her.