We establish integral tests and laws of the iterated logartihm for the upper envelope of the future infimum of positive self-similar Markov processes and for increasing self-similar Markov processes at $0$ an at $+\infty$. our proofs are based on the Lamperti transformation and time reversal arguments due to Chaumont and Pardo [9]. These results extend laws of the iterated logarithm for the future infimum of a Bessel process due to Khoshnevisan et al. [11].