In this paper, we investigate the downlink transmission of a multiuser multiple-input single-output (MISO) channel under a symbol-level precoding (SLP) scheme, having imperfect channel knowledge at the transmitter. In defining the SLP problem, a general category of constructive interference regions (CIR) called distance preserving CIR (DPCIR) is adopted. In particular, we are interested in the robust SLP design minimizing the total transmit power while satisfying the users' quality-of-service (QoS) requirements. We consider two common models for the channel uncertainty region, namely, norm-bounded spherical and stochastic. For the spherical uncertainty model, a worst-case robust precoder is proposed, while for the stochastic uncertainties, we define a convex optimization problem with probabilistic constraints. We simulate the performance of the proposed robust approaches, and compare them with the existing methods. Through the simulation results, we also show that there is an essential trade-off between the two robust approaches.