If I get you right, you are referring to the Predictive Performance of a calibrated model, calibrated using observed data. And you have used 'independent' data, not included in calibrating the model, to 'estimate' NSE etc as measures of predictive performance of the calibrated model to reliably predict the 'unobserved' / 'unforeseeable' future. The answer to your question does not appear to be simple and straightforward! There is a lot written on this subject - with no universal consensus on the issue. You can check past issues of hydrology journals to read more and to get some answers.

I agree with Dr.Chandra, the answer is not universal, and it depends upon what you want to project or estimate. But the permissible limit seems not to be SEE, I think it is better for an relative error index, such as TRE or MPE. Based on our studing results in forestry modeling, we presented 6 statistics for model evaluation, i.e., R^2, SEE, TRE, ASE, MPE, and MPSE. For perfect fit, R^2 is near to 1, TRE and ASE are near to 0, less SEE, MPE, MPSE are, better the model is. But in general, SEE is not near to 0, and MPE is related to sample size. We usually set a permissible limit for prediction error, such as 5% or 10%, which will be identified by MPE, TRE and ASE. For example, we want the prediction error of tree volume estimates not more than 3%, then for the developed tree volume model, MPE, TRE and ASE should be less than 3%. The expressions of the 6 statistics can be found in the attached file. Hope it is helpful.

To ascertain the permissible limits of the percent error, you may need to generate a three-way cross-tabulation between the type of   error (false negative rate and false positive rate), the groups of  stakeholders, and the future horizons (near, mid, and far term) for the cost to the stakeholders.