The aim of this paper is to derive representations of the modified Bessel functions of the first and the third kind of purely imaginary orders

${K}_{i\nu}\left(x\right)$ and

${I}_{i\nu}\left(x\right)$, respectively, in terms of non-oscillating integrals. Starting from two well-known integral representations of

${K}_{i\nu}\left(x\right)$ and

${I}_{i\nu}\left(x\right)$ [see

*G. N. Watson*, A treatise on the theory of Bessel functions (1944); p. 181, §6.22 (3) and (7)] in which

$\nu $ and

$x$ are assumed to be real,

$x>0$,

$\nu \ge 0$, and making use of certain paths of steepest descent (the saddle point contours), the author deduces interesting non-oscillating integral representations for

${K}_{i\nu}\left(x\right)$ and

${I}_{i\nu}\left(x\right)$. These representations can be useful for obtaining asymptotic expansions as well as numerical algorithms.