This invention is an improved tissue localizing device for fixedly yet removably marking a volume of tissue containing a suspect region for excision. This invention also encompasses methods for deployment of the localizing device and its excision along with the marked tissue volume. At least one locator element is deployed into tissue and assumes a predetermined curvilinear shape to define a tissue border containing a suspect tissue region along a path. The locator element path preferably encompasses the distalmost portion of the tissue volume without penetrating that volume. Multiple locator elements may be deployed to further define the tissue volume along additional paths defining the tissue volume border that do not penetrate the volume. Other localization wire embodiments of the invention are disclosed in which the tissue volume may be penetrated by a portion of the device. Polar and tangential deployment configurations as well as a locator element that may be cold-formed by a die in the distal portion of the deployment tube into a permanent arcuate shape are also disclosed.