Grammatical but Possibly Awkward
The example sentences in the question are not grammatically wrong. Adjectives are most often followed by nouns, but elided forms and various fixed phrases and idioms can alter that.
However, this sort of construction can be awkward, and often recasting it will improve and clarify the sentence. This depends very much on the specific sentence involved.
In this particular case I would not say that the first example sentence is awkward, much less wrong, but I think it could be improved. The second example, in part because of its complexity, does seem a bit awkward to me.
The form "at my/his/her best/worst" is a very common fixed phrase, and can be used freely. Other uses of this construction are less common, and may or may not work well.
Examples of the construction
- I like to visit Longwood Gardens in May, when they are at their most vibrant and beautiful.
- I recommend middle-period Heinlein, when he was at the top of his form.
- In election years, partisan outcries are at their most prevalent.
Recasting the original sentences
The originals might be recast as:
- She got married at 25 when she was at the height of her beauty.
She got married at 25 when she was more beautiful than at any other period of her life.
The meteorological data for 2000–2017, the period when the data were most reliable, were used in this study.
- The meteorological data for the period 2000–2017, for which highly reliable data are available, were used in this study.
These alternate versions seem to me to flow batter, but that is a matter of opinion. The originals are not wrong.