We present the results of an investigation of the X-ray and UV properties of four LINERs observed with Swift, aimed at constructing good S/N and strictly simultaneous UV-X-ray SEDs. In the current paradigm, LINER emission is dominated by geometrically thick, radiatively inefficient radiation flows (RIAFs) as opposed to radiatively efficient, geometrically thin accretion disks thought to power higher luminosity AGNs (Seyferts and QSOs). However, some recent studies have found more similarities than differences between the SEDs of LINERs and those of more luminous AGNs, suggesting that LINERs are powered by the same mechanisms active in higher luminosity AGNs. Our new observations allow us to test this idea. In particular, XRT affords long and sensitive monitoring of the X-ray emission. We detect significant variability in M81 and, for the first time, in NGC 3998. The maximum amplitude variations over time scales of some hours are 30% in both M81 and NGC 3998. NGC 3998 exhibits a variation of the same amplitude on a time scale of 9 days. M81 varies significantly over 2 years, with a maximum change of a factor 2 in 6 months. The X-ray variability detected in 2 of our sources, and in particular in NGC 3998, puts into question the interpretation of their powering mechanism as an inefficient accretion flow, because one of the characteristics of this model is the lack of variability. The identification of NGC 3998 with a low power AGN appears more viable.