Experimental data on the heat transfer coefficient during saturated flow boiling of CO$_2$ in a horizontal cylindrical tube (diameter 14 mm) with integrated metal sponges (open-cell metal foams) are presented in this publication. The nominal cell density of the sponges was 10 ppi (“pores per inch”) or 20 ppi. The mass flux varied from 25 kg m$^{-2}$ s$^{-1}$ to 125 kg m$^{-2}$ $,^{-1}$ and the vapor quality from 10% to 100%. The saturation pressure was either 12 bar, 19 bar or 26.5 bar. The length filled with sponge upstream of the heated part of the test section was 38 mm for the 10 ppi sponge and either 35 mm or 135 mm for the 20 ppi sponge. For the 20 ppi sample, the proportion of the test section filled with sponge was varied to investigate entrance effects. As a reference, the heat transfer coefficient during flow boiling in the empty tube was determined. In addition, geometric properties of the sponges relevant for the heat transfer coefficient (window diameter, strut diameter, porosity, specific surface area, and heat conductivity), were identified.