When initially reminding a customer about a past due payment, be sure to start your email by greeting your client to create a friendly tone. Throughout the email, remain polite and professional, and include a call to action (preferably with a link to where they can pay) to make it clear as to why you are contacting them. You can end your email with a classic sign off, such as 'sincerely' or 'best' to maintain the professional tone.
If the payment is only a few days past due, then you can avoid being stern with your client; however, once the payment because more than a month overdue, you may want to consider being a bit more direct in your follow up email.