This paper is concerned with the derivation of conforming and non-conforming functional a posteriori error estimates for elliptic boundary value problems in exterior domains. These estimates provide computable and guaranteed upper and lower bounds for the difference between the exact and the approximate solution of the respective problem. We extend the results from [5] to non-conforming approximations, which might not belong to the energy space and are just considered to be square integrable. Moreover, we present some numerical tests.