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The present work determines numerical solutions applied to flow problems in a cut-cell framework, introducing and evaluating two interpolation alternatives for the treatment of the convective terms and the effect of the variation of the number of slave cells generated near the solid interfaces. Using the upwind, QUICK and WAHYD (TVD) schemes, three benchmark cases were studied in the laminar regime, namely, flow between concentric cylindrical walls, flow in an inclined channel and flow around a cylinder. The numerical results obtained were favorable for the proposed interpolation methodology that prevents velocity over/under-estimations on the finite control volume faces, observing a tendency to produce smaller errors and mid-to-high computational efficiencies when coupled with a smaller number of slave cells generated at the boundaries. Although the magnitude of the errors found were small, improvements are of more significance for quantities that depend on gradient estimations at surfaces.