  We define a `non-relativistic conformal method', based on a Schr\"odinger
algebra with critical exponent z = 2, as the non-relativistic version of the
relativistic conformal method. An important ingredient of this method is the
occurrence of a complex compensating scalar field that transforms under both
scale and central charge transformations. We apply this non-relativistic method
to derive the curved space Newton-Cartan gravity equations of motion with
twistless torsion. Moreover, we reproduce z = 2 Ho\v{r}ava-Lifshitz gravity by
classifying all possible Schr\"odinger invariant scalar field theories of a
complex scalar up to second order in time derivatives.
