Photometric and spectroscopic observations of the faint Supernovae (SNe) 2002kg and 2003gm, and their precursors, in NGC 2403 and NGC 5334 respectively, are presented. The properties of these SNe are discussed in the context of previously proposed scenarios for faint SNe: low mass progenitors producing under-energetic SNe; SNe with ejecta constrained by a circumstellar medium; and outbursts of massive Luminous Blue Variables (LBVs). The last scenario has been referred to as ``Type V SNe, ``SN impostors or ``fake SNe. The faint SN 2002kg reached a maximum brightness of $mathrm{M_{V}=-9.6}$, much fainter than normal type II SNe. The precursor of SN 2002kg is confirmed to be, as shown in previous work, the LBV NGC2403-V37. Strong $mathrm{Fe II}$ lines are observed in the spectra of SN 2002kg, similar to both the LBV NGC2363-V1 and the type IIn SN 1995G. The spectrum of SN 2002kg does show strong resolved $mathrm{[N II]}$ at $lambdalambda$6549,6583ang. The identified progenitor of SN 2003gm is a bright yellow star, consistent with a F5-G2 supergiant. SN 2003gm, at the epoch of discovery, was of similar brightness to the possible fake SN 1997bs. Photometrically SN 2003gm shows the same decrease in brightness, over the same time period as SN 1997bs. The early time spectra of SN 2003gm are dominated by Balmer emission lines, which at the observed resolution, appear similar to SN 2000ch. On the basis of the post-discovery photometric and spectroscopic observations presented here we suggest that SN 2003gm is a similar event to SN 1997bs. The presence of strong $mathrm{[N II]}$ lines, near $mathrm{Halpha}$, is suggested as a possible means of identifying objects such as SN 2002kg/NGC2403-V37 as being LBVs - although not as a general classification criterion of all LBVs masquerading as SNe (abridged).
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