Monolithic [Cs0.05(MA0.17FA0.83)0.95]Pb(I0.83Br0.17)3/Cu(In,Ga)Se2 (perovskite/CIGS) tandem solar cells promise high performance and can be processed on flexible substrates, enabling cost-efficient and ultra-lightweight space photovoltaics with power-to-weight and power-to-cost ratios surpassing those of state-of-the-art III-V semiconductor-based multijunctions. However, to become a viable space technology, the full tandem stack must withstand the harsh radiation environments in space. Here, we design tailored operando and ex situ measurements to show that perovskite/CIGS cells retain over 85% of their initial efficiency even after 68 MeV proton irradiation at a dose of 2 × 1012 p+/cm2. We use photoluminescence microscopy to show that the local quasi-Fermi-level splitting of the perovskite top cell is unaffected. We identify that the efficiency losses arise primarily from increased recombination in the CIGS bottom cell and the nickel-oxide-based recombination contact. These results are corroborated by measurements of monolithic perovskite/silicon-heterojunction cells, which severely degrade to 1% of their initial efficiency due to radiation-induced recombination centers in silicon.