1 The headstone cleaning cost may vary depending on the age of the stone and its specific condition. 2  It is best to get an estimate of the cost so that you can choose a cleaning service that suits your budget. 3  Most of the cleaning services offer packages and you can choose per your personal preference. The rates are usually for three annual visits and you may have to pay extra if you want any additional service. 2  If you want a one-time headstone cleaning, the costs are usually around $20 to $50.