Here are the basic rules for starting and ending correspondence:

Note that in UK English, if you start with Dear Sir or Dear Madam, you should end with Yours faithfully. But if you use the person’s name, you should end with Yours sincerely. This rule may seem arbitrary, but it is one of the rules of formal letter writing that is widely known in the UK; therefore I recommend you stick to it. However, there is no such strict rule in the US.

Email writing is generally less formal than letter writing, but it is still a good idea to maintain a degree of formality in business correspondence, especially if you’re writing to someone you do not know. In such a case I would recommend starting an email with a phrase from the first two rows in the table above, but ending it with a phrase from the third row.  When you know the person you’re emailing — or have corresponded before — it is fine to use a starting phrase from the third row as well.

Here are some example closing sentences for emails:

I look forward to hearing from you.

I look forward to hearing from you soon.

I look forward to receiving your reply.

I look forward to seeing you.

I look forward to meeting you.

I look forward to speaking to you on this matter.

I look forward to a successful working relationship in the future.

Please let me know a convenient time for us to meet / for me to call you.

If you need any further information, please do not hesitate to contact me.

I will let you know more details as soon as I have them.

Please feel free to call me any time on my mobile: 0099 999 999 999

I would appreciate your immediate attention to this matter.

As this matter is urgent, I would be grateful for a swift response.

For more information on writing emails see: How to start emails