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Performing machine learning (ML) computation on private data while maintaining data privacy, aka Privacy-preserving Machine Learning~(PPML), is an emergent field of research. Recently, PPML has seen a visible shift towards the adoption of the Secure Outsourced Computation~(SOC) paradigm due to the heavy computation that it entails. In the SOC paradigm, computation is outsourced to a set of powerful and specially equipped servers that provide service on a pay-per-use basis. In this work, we propose SWIFT, a robust PPML framework for a range of ML algorithms in SOC setting, that guarantees output delivery to the users irrespective of any adversarial behaviour. Robustness, a highly desirable feature, evokes user participation without the fear of denial of service. At the heart of our framework lies a highly-efficient, maliciously-secure, three-party computation (3PC) over rings that provides guaranteed output delivery (GOD) in the honest-majority setting. To the best of our knowledge, SWIFT is the first robust and efficient PPML framework in the 3PC setting. SWIFT is as fast as (and is strictly better in some cases than) the best-known 3PC framework BLAZE (Patra et al. NDSS'20), which only achieves fairness. We extend our 3PC framework for four parties (4PC). In this regime, SWIFT is as fast as the best known fair 4PC framework Trident (Chaudhari et al. NDSS'20) and twice faster than the best-known robust 4PC framework FLASH (Byali et al. PETS'20). We demonstrate our framework's practical relevance by benchmarking popular ML algorithms such as Logistic Regression and deep Neural Networks such as VGG16 and LeNet, both over a 64-bit ring in a WAN setting. For deep NN, our results testify to our claims that we provide improved security guarantee while incurring no additional overhead for 3PC and obtaining 2x improvement for 4PC.