The process of "mending a gravestone" is far more complex than simply restoring a stone to it's previous condition. Performed correctly, cemetery restoration projects require careful observation, a scientific knowledge of the make-up of stone materials, an assessment of surrounding environmental conditions that have caused damage to the stone, and may do so again at some future date, sensitive treatment of fragile artifacts, and an understanding of art restoration.
Cemetery restoration is, in fact, not unlike an archaeological dig where, before any excavation is actually performed, a team of knowledgeable individuals combine their expertise to analyze and plan the delicate task of preservation.
The best example of this in my estimation, is "Monument Conservation Collaborative LLC," headed by Irving Slavid and his team of experts who have each worked in their field for years. They are located in CT, but work internationally. Without further explanation, I urge you to visit their website for a fascinating and comprehensive view of important cemetery restoration work. It's a very visually detailed site. Do not miss the article on their work at the beautiful Satala Cemetery, in American Samoa. You may read that article from here, but again, I urge you to visit this extensive, informative site.