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Cryoconite holes form on ice due to enhanced ablation around particles deposited on the surface, and are present in the ablation area of glaciers worldwide. Here we investigate the use of Ground Penetrating Radar (GPR) as a non-destructive method to monitor and map cryoconite holes. We compare GPR data obtained from the Jutulsessen blue ice area in Dronning Maud Land, Antarctica, with modeled GPR data. The modeled GPR response to cryoconite holes is numerically calculated by solving Maxwell's equations with a 3D Finite-Difference Time-Domain (FDTD) scheme. The model includes a realistic shielded bowtie antenna and dimensions and constituent parameters of cryoconite holes excavated in the field. We have performed what-if scenarios with controlled variation of single parameters. We show that GPR can be used to determine the horizontal extent, depth and whether a cryoconite hole is frozen or contains liquid water, information unavailable from visual surface inspection. The cryoconite thickness can, for completely frozen holes, be determined to within a 1/4 of the GPR center frequency wavelength. The exact water content is not readily extractable because the GPR response is influenced by many other factors such as: cryoconite thickness, shape and roughness, as well as antenna ground coupling.