Catholic cemeteries in any given location generally are owned or controlled by the diocese or archdiocese for that area. The good news is that all of the major dioceses and some not-so-major ones have web pages devoted to their Catholic cemeteries. But these websites vary in terms of the genealogical information one will find there. Most will at least include a note about the diocese's policies and procedures for genealogical research. My (less-than-scientific) canvass of diocesean procedures indicates that many will respond to mail requests for information and charge a small fee for the service. Many dioceses have PDF forms online for genealogical requests or direct email access for questions. But several dioceses have gone a step further, with searchable databases for their cemeteries.
Two of the better searchable databases can be found in the Archdiocese of St Louis and the Archdiocese of Milwaukee. Other U.S. dioceses with searchable cemetery records online include:
Archdiocese of Seattle
Diocese of Fresno (Calif.)
Diocese of Wilmington (Del.)(includes Eastern Shore of Maryland)
If you know of other sites with searchable databases of Catholic cemetery records, please share in the comments here.