Methods in accordance with aspects of this invention form microelectronic structures in accordance with other aspects of this invention, such as non-volatile memories, that include (1) a layerstack having a pattern including sidewalls, the layerstack comprising a resistivity-switchable layer disposed above and in contact with a bottom electrode, and a top electrode disposed above and in contact with the resistivity-switchable layer; and (2) a dielectric sidewall liner in contact with the sidewalls of the layerstack; wherein the resistivity-switchable layer includes a carbon-based material, and the dielectric sidewall liner includes an oxygen-poor dielectric material. Numerous additional aspects are provided.