We test the theory that lenticular (S0) galaxies form from spirals whose star formation has been shut down. We use the globular cluster specific frequency S_N, defined as the number of globular clusters normalised by the galaxy luminosity as a diagnostic. NTT/EMMI long-slit spectroscopic observations of 11 S0 galaxies at z < 0.006 are used to measure the absorption-line indices, Hdelta, Hgamma, Mgb, Fe5270 and Fe5335 within the central r_e/8. By inverting single-stellar population models, luminosity-weighted mean ages, metallicities and alpha-element abundance ratios are derived. We estimate the amount of fading a galaxy has undergone by comparing each galaxys S_N with its deviation from the mean spiral S_N. Galaxies with higher S_N have older stellar populations. Moreover, we find that the zero-point and amount of fading is consistent with a scenario where lenticulars are formed by the quenching of star formation in spiral galaxies. Our data also rule out any formation method for S0s which creates a large number of new globular clusters. We confirm that previous results showing a relationship between S_N and color are driven by the S_N - Age relation. Five galaxies show detectable Hbeta, [OIII], Halpha or [NII] emission lines. However, only in the two youngest galaxies is this emission unambiguously from star formation. Our results are consistent with the theory that S0 galaxies are formed when gas in normal spirals is removed, possibly as a result of a change in environment. The on-going star formation in the youngest galaxies hints that the timescale of quenching is ~< 1 Gyr. We speculate, therefore, that the truncation of star formation is a rather gentle process unlikely to involve a rapid burst of star formation.
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