In general, perturbative expansions of observables in powers of the coupling constant in quantum field theories are asymptotic series. In many cases it is possible to apply resummation techniques to assign a unique finite value to an asymptotic series, but a particular pattern of divergence, the so-called renormalon, gives rise to non-perturbative ambiguities. The framework of Numerical Stochastic Perturbation Theory (NSPT), based on stochastic quantisation and the perturbative expansion of lattice fields, makes it possible to compute coefficients of perturbative series on the lattice. In this work we report on an NSPT study of asymptotically free sigma models, namely the Principal Chiral Model and the $\text{CP}(N-1)$ model. We present results for a lattice computation of the expansion coefficients of the energy density and discuss signatures of renormalons.