Let G be a second countable, locally compact group and let f be a continuous
Herz-Schur multiplier on G. Our main result gives the existence of a (not
necessarily uniformly bounded) strongly continuous representation on a Hilbert
space, such that f is the coefficient of this representation with respect to
two vectors with bounded orbit. Moreover, we show that the norm of the
representation of an element g from G is at most exponential in terms of the
metric distance from g to the identity element of G.