Composite ab initio methods based on local coupled-cluster approaches calculate the CCSD(T)/CBS energy at a significantly reduced computational cost than the corresponding canonical methods. While showing promising performance for general thermochemistry, local composite ab initio methods have not been tested for fullerenes. Here we examine the performance of several local G4(MP2)-based methods for calculating the relative stability of a diverse set of C40 fullerenes. We use canonical G4(MP2) isomerization energies as reference data. Fullerenes provide a challenging problem for DLPNO-G4(MP2)-based methods. The DLPNO-based methods result in overall root-mean-square deviations (RMSDs) of 28.6 (NormalPNO with CCSD(T0)), 23.0 (NormalPNO with CCSD(T1)), and 16.1 (TightPNO with CCSD(T0)) kJ mol−1. The local natural orbital LNO-G4(MP2) method provides the best overall performance with an RMSD of 4.9 kJ mol−1. The DLPNO-G4(MP2) and LNO-G4(MP2) methods systematically overestimate the canonical G4(MP2) isomerization energies. Therefore, they provide valuable upper limits of the fullerene isomerization energies.