This report reviews the issues concerning data curation for heritage science. It provides a policy framework to be implemented by E-RIHS, but the report is designed to be of use to all those with interests in data within the heritage science domain. E-RIHS provides an opportunity to ensure the long term preservation and increased re-use of heritage science data within broader European frameworks. The report follows the structure of the FAIR principles (Findable, Accessible, Interoperable and Re-usable) but interprets them in the context of heritage science. Examples are given with reference to a substantial appendix which covers a broad range of heritage science data types. It is recommended that E-RIHS researchers should be required to complete a Data Management Plan as a condition of support for their usage of an E-RIHS facility, and this, along with the information contained in this report, will assist E-RIHS researchers, facilities and repositories to follow our thirty-three recommendations.