To boil: Scrub potatoes and simmer until just tender, drain, cool and quarter and leave until ready to grill.
To Microwave: Scrub and quarter potatoes lengthways. Put in a microwave proof oven bag with 2 tablespoons butter and 2 tablespoons water. Fasten bag with a rubber band leaving a finger sized opening for steam. Microwave on full power for 12-20 minutes, repositioning potatoes in the bag twice, until potatoes are barely tender. Leave potatoes in bag until ready to grill.
Put the potato quarters on a preheated oiled grill rack or plate, and turn to brown all sides evenly, brushing with flavored butter or oil only if they burn.