I think it would be useful to have an international standard to refer to when evaluating if an quantitative theoretical model is reliable. Unfortunately no such standard exists.
If we regard the case where the theoretical model is about predicting the quantity of an output value for a number of inputs. There are some standards relating to measurement, uncertainty and testing that are relevant. Among these are: International Standardization Organisation ISO: Guide to the expression of uncertainty in measurement, General requirements for the competence of testing and calibration laboratories; And Bureau International des Poids et Measure BIPM: International vocabulary of metrology
Based on these standards – I regard it reasonable to expect from an useful and reliable theoretical model that it fulfills the criteria:
- The theory is about a causal relations between quantities that can be measured
- The measurands are well defined
- The measurands can be quantified within a reasonable uncertainty
- The uncertainty of the measurands has been determined by statistical and / or quantitative analysis
- The functional relationships, the mechanisms, has been explained in a plausible manner
- The functional relationships, the mechanisms, has been expressed in mathematical terms
- The functional relationships between variables and parameters has been combined into a model.
- The influencing variables which have significant effect on the accuracy of the model are identified
- The model has been demonstrated to consistently predict outputs within stated uncertainties
- The model has been demonstrated to consistently predict outputs without significant systematic errors
- The model has been tested by an independent party on conditions it has not been adjusted to match
I would also expect that data, methods, models and test results are readily available for scrutiny, and that all information is provided in a way that is consistent with established standards.