A hyperbolic monopole is a certain configuration of $SU(2)$ fields in hyperbolic $3$-space, and has two basic numbers associated to it: a positive integer $k$, called the magnetic charge, and a positive real $m$ called the monopole mass. To a hyperbolic monopole, one can associate a spectral curve, which is (generically) a compact Riemann surface of genus $(k-1)^2$ encoding all the information about the fields. In this talk, I will describe joint work with Paul Norbury clarifying how one can compute the mass $m$ from a given spectral curve. I shall be discussing two classes of examples for which this calculation can be made quite explicit: (i) monopoles of charge $k=2$; (ii) monopoles with the symmetry of a platonic solid.