The gist of the article is that monetary fines and late fees are okay in certain circumstances:
"...pecuniary fines, as well as the destruction and seizure of property, are a permissible form of discretionary punishment. Such punishments can be effective in preventing and discouraging crimes that are harmful to society. Consequently, those punishments play a positive role in safeguarding the public welfare – the lives, property, and rights of the people.Read the whole article here.
Allah says: “O you who believe, obey Allah and obey His Messenger and those in authority among you.” [Sûrah al-Nisâ’: 59] As for the question of increasing the amount of punitive fines in the case of late payment, this is also permissible. In the case of a traffic fine, for example, this could be understood as setting two rates: a lower rate for paying on time and a higher rate for late payment.
However we choose to understand the increase in the fine, it is not a case of interest. This is because interest only occurs when there is an exchange of wealth, like in a purchase or a sale. This is not the case with pecuniary fines. There is no trade or commerce going on. The fine is nothing other than a form of punishment."
Financial transactions are a sensitive issue in Islam, so I would probably seek more clarification from a person of knowledge before implementing late fees for my writing business. If you ever find yourself in this situation, you can ask more specific questions from the Fatwa Department at IslamToday.com.
ETA: Here is an opposing view stating that late fees are prohibited by Islam.