We address the detection of unstable periodic orbits from experimentally me
asured transient chaotic time series. In particular, we examine recurrence
times of trajectories in the vector space reconstructed from an ensemble of
such time series. Numerical experiments demonstrate that this strategy can
yield periodic orbits of low periods even when noise is present. We analyz
e the probability of finding periodic orbits from transient chaotic time se
ries and derive a scaling law for this probability. The scaling law implies
that unstable periodic orbits of high periods are practically undetectable
from transient chaos.