We determine, experimentally and numerically, the electric and magnetic Purcell factors in a fishnet metamaterial in the frequency range 5–15 GHz by measuring the impedance of a dipole antenna. We compare measurements and numerical simulations of the Purcell factor for transverse electric (TEz) and transverse magnetic (TMz) polarizations. For TMz polarization, the dispersion relation of the structure is hyperbolic and enhances the Purcell factor. For TEz polarization, the dispersion relation does not allow any propagating solutions and decreases the Purcell factor below the effective plasma frequency. Eigenmode calculations of the periodic unit cell of the metamaterial are used to obtain the band structure and confirm the presence of hyperbolic isofrequency surfaces. The isofrequency surfaces are used to calculate the density of states (DOS). We also use the impedance method to obtain the DOS by averaging the Purcell factor obtained at different locations over the periodic unit cell and find good agreement with DOS calculated from eigenmode calculations.