QNH1013, you don't need GPS to be RVSM-certified. There are lots of planes around without GPS which are certified so far. You need to have an airplane which has the required vertical navigation performance capability required for RVSM operations in compliance with the MASPS. But that should be in your RVSM-Training/Ops-Manual. The main things are two independent altimeter systems, an automatic altitude control system (aka autopilot) and at least TCAS/ACAS version 7.0.