I'd go further and consider just complimenting the person face-to-face and leave it at that. Help them understand their true value and that they should make sure they're not undervaluing themselves in terms of compensation or satisfaction.

That level of employee is either already recognized or they have idiots for managers. Praising them to an idiot boss probably just causes them more problems (jealousy for one or some point of praise gets twisted as them not following protocol -- maybe a report was late because they spent "too much" time with customers). If you go ahead, I agree with another commenter who said direct the feedback as high as possible to prevent jealousy or other backfire.

I'd agree with the manager approach if the person was so low level that it would be easy for their contribution to be missed.

When I'm complimented by a client verbally, I politely give them my manager's email address and ask them to forward that information on. I find that I've gotten a number of compliments that I compile for my yearly performance review. I like my client and my manager, and while it may not affect my compensation (I get regular, small increases), it seems to keep negative micro-management from affecting my day-to-day work, and feeds the cycle of positive feedback that allows me to do interesting work, instead of defending how my hours are spent.

I'd encourage positive communication between clients and managers. My dad had a lot of good things to say about his military service. One of them was cultural: tell the guy what he could do better. Tell his superior what he's done well.

This is critical. Worse still, they might be trying to not be a squeaky wheel for any number of reasons. Giving them attention from higher-ups might not be so positive in their eyes.