Research is an institution. Just qualify the uncertainty and describe your further work to investigate.
The peaks in your spectra, the calculation results, or the microscopy image either support your findings or they don't, so P-values don't get as much milage. I can't remember the last time I saw a P-value in one of those papers.
This does create a problem similar to publishing null result P-values, however: if a reaction or method doesn't work out, journals don't want it because it's not exciting. So much money is likely being wasted independently duplicating failed reactions over and over because it just never gets published.