How to do evaluation when the methodology is unique?
TL;DR: if you don't know how to evaluate your work, you probably don't know exactly what research question you are working on.


  How would we perform evaluation for methods that can't be compared against others?


I work in applied computer science, and this qualifies as the Number One statement my master students usually have when I ask them how they plan to evaluate their work - "I can't compare my tool / approach against anything - no existing tool has exactly the same scope, so the comparison won't be fair!".

This is of course true, but it also shows a misunderstanding about the research question that the work is addressing. Essentially, the "compare against a standard tool" approach is a valuable evaluation method if the research question is "Can we improve the performance/quality/whatever of an approach that does X?". If the research question is rather, as presumably in your case, "Can we find an approach that does X?", the evaluation of course needs to be different.

In that case, you need to find an evaluation that actually shows what you claim your approach does. Some recent examples from my students:

Is your claim that it makes sense to show software developers certain information, which isn't visualized by any other development tool? In that case you need to set up a study where you show that developers that see this piece of information do something better than developers that don't. Is your claim that taking costs of cloud resources into account when scheduling tasks allows for cheaper execution with the same quality? Set up an experiment where you compare costs with and without taking costs into account for a number of representative workloads.

Orthogonally, it often makes sense to do a partial comparison to existing approaches and tools, to also check how your approach fares in comparison to standard tools on standard problems, essentially to make sure that the improvement your approach presumably has in a "new" dimension does not mean that something else does not work anymore. For instance, in the development tool example above, you may also want to check if the new visualization distracts people so much that they now fare less well in usual development tasks than with standard tools.