A magnetically recyclable eggshell-based catalyst (MKEC) was synthesized to circumvent saponification during the conversion of neem, Jatropha, and waste cooking oils (free fatty acid, 2.3–6.6%) to biodiesel. The characterization results indicated that MKEC had a mesoporous structure with the pore width of 3.24 nm, a specific surface area of 128 m²/g, and a pore volume of 0.045 cm³/g. The results confirmed that the MKEC is more tolerant to fatty acid poisoning than calcined eggshell. The effects of process parameters for maximum fatty acid methyl ester (FAME) content were evaluated by central composite design (CCD) and artificial neural network (ANN). The experimental FAME content of 94.5% was achieved for neem oil with a standard deviation (SD) of 0.68, which was in reasonable agreement with predicted values (CCD, 96.9%; ANN, 95.9%; SD, 0.73). The reusability studies showed that the mesoporous catalyst can be reused efficiently for five cycles without much deterioration in its activity.