Extremely high removals of total suspended solids and oil and grease were obtained when olive mill wastewaters were filtered using new silicon carbide tubular membranes. These new membranes were used at constant permeate flux to treat real olive mill wastewaters at pilot scale. The filtration conditions were evaluated and optimized in terms of the selection of the permeate flux and flux maintenance strategies employed—backpulsing and backwashing—in order to reduce fouling formation. The results obtained reveal that the combination of backpulses and backwashes helps to maintain the permeate flux, avoids transmembrane pressure increase and decreases the cake resistance. Moreover, membrane cleaning procedures were compared and the main agents responsible for fouling formation identified. Results also show that, under total recirculation, despite an increased concentration of pollutants in the feed stream, the quality of the permeate is maintained. Membrane filtration using silicon carbide membranes is an effective alternative to dissolved air flotation and can be applied efficiently to remove total suspended solids and oil and grease from olive mill wastewaters.