The application of additively manufactured templates during manufacturing of ceramic foam filters for metal melt filtration using the replica technique has considerably extended the scope for the design of improved filter geometries. While the production and testing of novel filters in real trials is time-consuming and expensive, virtual prototyping allows the generation and screening of a huge number of variants at comparatively low cost. For the present study, an automated workflow for the computer generation and efficient evaluation of novel filter geometries has been developed. Three different geometric modifications to a reference foam structure were considered: the elliptical elongation and flattening of the strut cross section obeying a prescribed aspect ratio, the addition of finger-like struts protruding into the pore, and the deliberate closing of pore windows. All modifications were parametrically varied and implemented for macroscopic porosities between 70 % and 90 %, resulting in a total of 45 geometry variants. The different structures were characterized by the relevant hydraulic effective properties, namely, the hydraulic tortuosity, the permeability and the Forchheimer coefficient, which have been obtained from detailed pore-scale simulations of the flow field using the lattice-Boltzmann method. In order to assess the filtration performance, the filtration coefficient has been evaluated for conditions present during continuous casting of aluminium employing Lagrangian tracking of inclusions. Among all modifications which improve filtration, the addition of finger-like struts is associated with the smallest increase in pressure gradient, rendering it the most efficient measure, while the partial closing of windows is the least efficient one. A comparison of the filtration coefficient with different geometric and hydraulic effective properties for all samples shows a correlation with the hydraulic tortuosity and also the inverse of Forchheimer coefficient, but no consistent correlation with the specific surface area.