A large diameter corkscrew is inserted into a cork, or into the remaining portion of a broken cork, so that the cork can be extracted through the top of the wine bottle without contacting the wine. In one example, the large diameter corkscrew has a diameter of about 17 mm, as opposed to approximately 8 mm for conventional corkscrews. This larger diameter permits the corkscrew to be inserted into the cork in its unbroken periphery, as opposed to attempting to insert a corkscrew into the debris in the center of a broken cork. In one example, the large diameter corkscrew has a cross section with a flat, angled top portion and a tapered lower portion. This non-circular cross section provides a relatively large contact area for engaging the cork, while providing a reduced cross section area to minimize cork breakage as the corkscrew is inserted into the cork.