An experimental investigation of the unsteadiness boundary for supersonic flow over a double cone in a geometrical space of the first and second cone angles ( \(\theta _1\) and \(\theta _2\) ) identified numerically by a previous study is made using the Caltech Ludwieg tube operating at Mach 4. Eleven double cone geometries near the upper and lower branches of the unsteadiness boundary were selected. Qualitative high-speed schlieren imaging and shock tracking analysis techniques were employed. The experimental boundary agreed well with the prior computational study, except for one case that experienced unsteadiness when \(\theta _2\) was less than the second cone detachment angle. Unsteady cases on the lower branch of the boundary experienced mild oscillations primarily confined to the leading cone shock and triple point while unsteady cases on the upper branch exhibited more violent, pulsating unsteadiness. Four geometries were tested over a range of Reynolds numbers (8.3–24.8 million/m) and verified the unsteadiness behavior is not influenced by changes in Reynolds numbers in this range.