Let A be an n X m matrix with m > n, and suppose the underdetermined linear system As = x admits a unique sparse solution s0 (i.e. it has a solution s0 for which ks0k0 < 1 2 spark(A)). Suppose that we have somehow a solution (sparse or non-sparse) ^s of this system as an estimation of the true sparsest solution s0. Is it possible to construct an upper bound on the estimation error k^s - s0k2 without knowing s0? The answer is positive, and in this paper we construct such a bound which, in the case A has Unique Representation Property (URP), depends on the smallest singular value of all n X n submatrices of A.