This paper presents a generic “GMW-style” method for turning passively secure protocols into protocols secure against covert attacks, adding relatively cheap offline preprocessing and post-execution verification phases. Our construction performs best with a small number of parties, and its main benefit is the total cost of the online and the offline phases. In the preprocessing phase, each party generates and shares a sufficient amount of verified multiplication triples that will be later used to assist that party’s proof. The execution phase, after which the computed result is already available to the parties, has only negligible overhead that comes from signatures on sent messages. In the postprocessing phase, the verifiers repeat the computation of the prover in secret-shared manner, checking that they obtain the same messages that the prover sent out during execution. The verification preserves the privacy guarantees of the original protocol. It is applicable to protocols doing computations over finite rings, even if the same protocol performs its computation over several distinct rings. We apply our verification method to the Sharemind platform for secure multiparty computations (SMC), evaluate its performance and compare it to other existing SMC platforms offering security against stronger than passive attackers.