Several quantities relevant to phenomenological studies of B-0-(B) over bar (0) mixing are computed on the lattice. Our main results are f(Bd) root(B) over cap (Bd) = 206(28) (14)(-00)(+31) MeV, xi = f(Bd) root(B) over capB(x)/f(Bd) root(B) over cap (Bd) = 1.16(7). We also obtain the related quantities f(Bs) root(B) over cap (Bs) - 237(18) (10)(-00)(+34) MeV, f(Bd) = 174(22)(-0-0-00)(+7+5+26) MeV, f(Bs) = 204(15)(-0-0-00)(+7+4+31) MeV, f(Bs)/f(Bd) = 1.17(4)(-1)(+0), f(Bd)/f(Ds) = 0.74(5). After combining our results with the experimental world average Deltam(d)((exp)), we predict Deltam(s) = 15.8(2.1)(3.3) ps(-1). We have also computed the relevant parameters for D-0-(D) over bar (0) mixing which may be useful in some extensions of the Standard Model. All the quantities were obtained from a quenched simulation with a non-perturbatively improved Clover action at beta = 6.2, corresponding to a lattice spacing a(-1) = 2.7(1) GeV, on a sample of 200 gauge-field configurations. A discussion of the main systematic errors is also presented. The quenching errors are not included in the systematic error estimates.