1998 Honda Civic shuttering at high speeds while braking

1998 Honda Civic 4 cyl 110000 miles

My Civic shutters when I brake going 70 mph. The steering wheel shakes but the brake itself does not shake. It also seems to slow inconsistently. When I come to a stop there is are several instances where the car seems to want to go forward while I'm braking. The intervals of this seem very consistent as I slow. It feels like there is something wrong with the brakes, but I have taken both the front and rear brakes off and there seems to be no irregularities.