Low resistance contacts to epitaxial n-CdTe on InSb have been formed by excimer laser induced diffusion of In with subsequent deposition of gold. Diodes have been fabricated using a combination of laser processing and conventional photolithigraphy, and the forward bias and reverse bias current-voltage characteristics measured. All the diodes behaved effectively as Schottky diodes with high ideality factors (n approximate to 3) and exhibited stable characteristics over several months. Estimates of the Zn-CdTe barrier height have been made taking into account the effective current dependent series resistance which is known to arise from the rear InSb-CdTe junction. The barriers range from 0.7 eV (no diffusion) to 0.4 eV, the last having a specific contact resistance of 0.16 Omega/cm(2). We shaw from the characteristics of the rear junction, together with an estimate of the maximum melt-depth, that In has not diffused to the rear InSb-CdTe junction.