A simple renewal process is a stochastic process $\left\{X_n\right\}$ taking values in $\{0,1\}$ where the lengths of the runs of $1$’s between successive zeros are independent and identically distributed. After observing $X_0,X_1,...X_n$ one would like to estimate the time remaining until the next occurrence of a zero, and the problem of universal estimators is to do so without prior knowledge of the distribution of the process. We give some universal estimates with rates for the expected time to renewal as well as for the conditional distribution...