  The majority of renormalizable field theories possessing the scale invariance
at the classical level exhibits the trace anomaly once quantum corrections are
taken into account. This leads to the breaking of scale and conformal
invariance. At the same time any realistic theory must contain gravity and is
thus non-renormalizable. We show that discarding the renormalizability it is
possible to construct viable models allowing to preserve the scale invariance
at the quantum level. We present explicit one-loop computations for two toy
models to demonstrate the main idea of the approach. Constructing the
renormalized energy momentum tensor we show that it is traceless, meaning that
the conformal invariance is also preserved.
