What Is The Best Way To Cook Rump Steak?

All cheaper cuts of beef benefit from marination (red wine or red vinegar in the marinade will soften and break down the tendons) and the slow cooking or roasting.  If you want to grill it, do so at a low temperature and leave it on the grill for a long period of time.

Flash grill it at a high temperature to seal the surface and get those nice burnt BBQ stripes, then cook long and slow in the oven with a foil cover. That way, you get the BBQ flavour plus a tender steak. Rump has much more flavour than fillet, but it does need slow cooking to keep it tender.

Make sure your steak is at room temperature.  Marinade it, drain off the marinade, put under a very hot grill to seal  each side then turn the temperature down.  Cook to how you like it.  Allow it to stand to become even more tender.