A real tip is handed to the gal at the end of the session so she gets the message loud and clear that she really rocked.

But as someone who does often tip, I thank you.

The best way to show appreciation is to really turn it on the next time you meet.

No, you should not call, txt, or email unless they have indicated they have a private account & it's ok to leave a message.  A text is what got Tiger in trouble!  If in doubt, DON'T!

IF you have permission to leave a message, then it would be very nice to send a brief "thank you for your generosity" message.  It would be appreciated.  

When I contact a lady, I inform them that [email protected] is my private e-mail & (XXX)XXX-XXXX is my private phone & ok to leave a message.
skb

ooo thank you for asking this question..I too, have often been in the same circumstances and never know what to do after the fact...

If it appears they have an anonymous email account, a discreet email showing your appreciation is fine. If they use a personal account, don't do it.

On a side note:

From checking your website, I think your rates are too low for the service you provide. It is the easiest explanation for why some clients are tipping you double your rate.

This is what I would do. Research experienced providers in your area and see what the "market rate" is for like services. Adjust your rate accordingly.

Make it clear to your existing clients, that their rates are "grandfathered" meaning your old rates still apply to them. If you continue to provide them the same great service, in all likely hood they will continue to double tip you.

I tip at the end of the session usually, so it's not an issue, but there are times when they didn't realize I tipped and a got a quick call (on my way home) or email to say thanks. I always thought that was a nice touch. I have a hobby email account so emails are always the best way to do that in my opinion.

Assuming the date was set up by e-mail, send him a quick thank you through that medium.  Phone calls can be tricky unless he has a hobby phone and can take calls (or let them go to VM) without consequences.