  Operation of Josephson electronics usually requires determination of the
Josephson critical current $I_c$, which is affected both by fluctuations and
measurement noise. Lock-in measurements allow obviation of $1/f$ noise and,
therefore, provide a major advantage in terms of noise and accuracy with
respect to conventional dc-measurements. In this work we show both
theoretically and experimentally that the $I_c$ can be accurately extracted
using first and third harmonic lock-in measurements of junction resistance. We
derive analytic expressions and verify them experimentally on nano-scale
Nb-PtNi-Nb and Nb-CuNi-Nb Josephson junctions.
