HS-125 Captain reported an electric trim failure caused vertical oscillations; which resulted in an autopilot failure. The flight crew elected to descend out of RVSM airspace and continued the flight to destination airport.

Narrative

A few minutes after achieving cruise altitude; in level flight on autopilot; the airplane began to softly porpoise. I noted to the Co-Captain; Hey; do you see this mountain wave?" We had just left ZZZ where we found quite a bit of turbulence. We thought the pitch changes and the feel of mountain wave off of the mountain range was what we were feeling. Finally; the airplane still on autopilot; took a couple more oscillations; each getting more aggressive and producing a climb and descent rate of up to 500 FPM. We called out to Air Traffic Control to make them aware that we were having trouble maintaining altitude due to turbulence. Just as my Co-Captain made the call; the airplane made an aggressive pitch up and tried to leave altitude. I instantly turned off autopilot and regained control. When I had the airplane in my hands; I could tell that it needed nose down trim. This is when I realized that the electric trim system had failed; causing the airplane to lose control of pitch. We immediately notified ATC that we in fact lost the electronic trim and autopilot. They responded and offered any assistance we would need. Ultimately; I flew the remainder of the short trip outside of RVSM by hand and landed at our home base without incident. The airplane has been checked into Maintenance and is scheduled for repair prior to any passenger flights. In recovery of the loss of electric trim; I believe the airplane reached 300 [ft.] above assigned altitude before I was able to bring it back down to the assigned FL260. I could have stopped it sooner but I did not know if the passengers (X) were seated; in the bathroom or whatnot; so I could not be too aggressive in the recovery because I did not want to send them into a "negative" G-loading; possibly sending them into the ceiling of the aircraft."