The National Institute of Standards and Technology, which is the national metrology institute of the USA, assigns certified values to the mass fractions of individual elements in single-element solutions, and to the mass fractions of anions in anion solutions, based on gravimetric preparations and instrumental methods of analysis. The instrumental method currently is high-performance inductively coupled plasma optical emission spectroscopy for the single-element solutions, and ion chromatography for the anion solutions. The uncertainty associated with each certified value comprises method-specific components, a component reflecting potential long-term instability that may affect the certified mass fraction during the useful lifetime of the solutions, and a component from between-method differences. Lately, the latter has been evaluated based only on the measurement results for the reference material being certified. The new procedure described in this contribution blends historical information about between-method differences for similar solutions produced previously, with the between-method difference observed when a new material is characterized. This blending procedure is justified because, with only rare exceptions, the same preparation and measurement methods have been used historically: in the course of almost 40 years for the preparation methods, and of 20 years for the instrumental methods. Also, the certified values of mass fraction, and the associated uncertainties, have been very similar, and the chemistry of the solutions also is closely comparable within each series of materials. If the new procedure will be applied to future SRM lots of single-element or anion solutions routinely, then it is expected that it will yield relative expanded uncertainties that are about 20 % smaller than the procedure for uncertainty evaluation currently in use, and that it will do so for the large majority of the solutions. However, more consequential than any reduction in uncertainty, is the improvement in the quality of the uncertainty evaluations that derives from incorporating the rich historical information about between-method differences and about the stability of the solutions over their expected lifetimes. The particular values listed for several existing SRMs are given merely as retrospective illustrations of the application of the new method, not to suggest that the certified values or their associated uncertainties should be revised.