A new constant contact pressure (CCP) indentation creep method is presented, which is based on keeping the mean contact pressure as defined through Sneddon’s hardness constant, until a steady-state strain rate is achieved. This is in contrast to the conventional constant load–hold (CLH) creep experiments, where the load is held constant and relaxation in both hardness and strain rate occurs at the same time. Besides controlling the mean contact pressure, the dynamic stiffness is furthermore used to assess the indentation depth, thereby minimizing thermal drift influence and pile-up or sink-in effects during long-term experiments. The CCP method has been tested on strain rate sensitive ultrafine-grained (UFG) CuZn30 and UFG CuZn5 as well as on fused silica, comparing the results with those of strain rate jump tests as well as the CLH nanoindentation creep tests. With the CCP method, strain rates from 5 × 10−4 s−1 down to 5 × 10−6 s−1 can be achieved, keeping the mean contact pressure constant over a long period of time, in contrast to the CLH method. The CCP technique thus offers the possibility of performing long-term creep experiments while retaining the contact stress underneath the tip constant.