How would you handle a situation where a customer has asked for some service or product that is in violation of the company’s policies?

It is very easy in this scenario !

Either the company policy or the customer's intention has some flaw !

You must be in a position to distinguish this through your wisdom to address diligently. 

Explain in a polite way and full of respect, so that the customer will not get opended..

I would thank and acknowledge the customer for visiting our company. Next I would listen to the request. in this case since its not offered in our company, I will apologize for not offering the service as required and explain  its not in our policy. However, I will go ahead to explain the service or products we offer and check if the customer will be interested to try what we have to offer.

Customer care guy first aware all of the company policies & then the guy will be able to answer of the customer question. Most of the customer care executives are not aware about the policies & limitations & sometimes they misguided to the customer. Customer executive needs to be addressed the all issues & try to explain the company policy in appropriate manner. so that customer could feel the situation.

Explain to he/she why this issue is considered as violation. mostly to protect your company and the client at the same time.

Politely explain and decline...................................

I will explain to the customer politely that as much as I would want to satisfy his or her needs, we still have a company policy we need to follow in order to have a smooth and successful transaction for both of us.

First, I will target his satisfaction using diplomatic speech then I'll compromise with his needs after company approval.