  We use a sample of submillimetre-selected galaxies (SMGs) with molecular gas
and dynamical mass measurements from the literature to put constraints on the
contribution of such galaxies to the total metal budget. Compared to Lyman
break galaxies (LBGs), for example, SMGs are rarer (by a factor of 10 or more),
but contain much more gas and are more metal rich. We estimate that SMGs
brighter than 3 mJy contain only less than 9% of the metals when we combine the
observed dynamical masses (few$\times 10^{11}$ \msun), number density ($n\simeq
10^{-4}$ Mpc$^{-3}$), observed gas metallicity (1--2 x solar), and observed gas
fractions (~40%) assuming a molecular to neutral hydrogen ratio of 1. Including
SMGs fainter than 3 mJy, we estimate that SMGs contain at the most 15% of the
metals, where our incompleteness correction is estimated from the dust mass
function. Our results are strong upper limits given that high gas fractions and
high overall metallicity are mutually exclusive. In summary, SMGs make a
significant contribution to the metal budget (< 15%) but not sufficient to
solve the `missing metals problem.' A consequence of our results is that SMGs
can only add $\approx 3.5$% to $\Omega_{\rm DLA}$, and can not be the source of
a significant population of dusty DLAs.
