Calcite (the most stable form of CaCO3) is a common mineral that naturally exists in geology and biology, and can also be grown synthetically. In its pure and defect-free form, calcite is relatively soft and brittle. Amazingly though, despite its intrinsic shortcomings as a structural material, calcite often serves a structural purpose in biology. For example, the teeth, shells, and spines of many marine organisms contain, or are entirely composed of, calcite. These biogenic calcite-containing structures are much stronger and tougher than a pure control calcite crystal, and small-scale indentation testing suggests that even the single-crystals of calcite that make up these structures may be significantly harder than a pure control. The exact mechanisms of the increased hardness are not known, thus there is much interest in creating model synthetic calcite crystals to replicate and help explain such hardening effects. However, it is difficult to interpret the differences in hardness between different biogenic and synthetic calcites because the reference hardness of pure single-crystal calcite is not well known (there are large variations in previously-reported data). In this work, strides are made towards achieving a better understanding of the strengthening of biogenic and synthetic calcites in three ways: (1) Previous reports of the indentation hardness of calcite are compiled and compared, and new experiments are performed to quantify the effect of the indentation size effect and crystal anisotropy on hardness measurements of calcite. (2) A new indentation method is developed that allows for accurate measurements to be made on small, embedded particles (like biogenic and synthetic calcite crystals), by accounting for the effect of a dissimilar matrix material. And (3) it is demonstrated that the hardness of pure synthetic calcite crystals can be increased by simply varying the kinetics of their growth. Additionally, previously published collaborative work (included in the Appendix) explains an important impurity-based strengthening mechanism in calcite.