Embolisation (you'll also see coiling, coil embolisation, or in the US embolization) is the main treatment for ovarian vein reflux: an interventional radiologist steers a thin catheter into the faulty vein through a tiny puncture and closes it from within — typically with small metal coils, often plus a foam or liquid agent for the surrounding network.
Closing a vein sounds drastic; the anatomy makes it routine. The pelvis drains through many parallel veins, so blood immediately reroutes through healthy ones — the procedure removes a leak, not a necessary pipe. It's a day procedure under sedation, and relief typically builds over weeks to a few months rather than overnight.
The full picture — what the day is like, recovery, honest answers to the coil worries, results data — is in embolisation: what actually happens, and if pain persists afterwards, that has its own map.