In this note, we discuss fast randomized algorithms for determining an admissible solution for robust linear matrix inequalities (LMIs) of the form F(x, Delta) less than or equal to 0, where 0 is the optimization variable and Delta is the uncertainty, which belongs to a given set Delta. The proposed algorithms are based on uncertainty randomization: the first algorithm finds a robust solution in a finite number of iterations with probability one, if a strong feasibility condition holds. In case no robust solution exists, the second algorithm computes an approximate solution which minimizes the expected value of a suitably selected feasibility indicator function. The theory is illustrated by examples of application to uncertain linear inequalities and quadratic stability of interval matrices.