Many genetically encoded biosensors use Förster resonance energy transfer (FRET) to dynamically report biomolecular activities. While pairs of cyan and yellow fluorescent proteins (FPs) are most commonly used as FRET partner fluorophores, respectively, green and red FPs offer distinct advantages for FRET, such as greater spectral separation, less phototoxicity, and lower autofluorescence. We previously developed the green-red FRET pair Clover and mRuby2, which improves responsiveness in intramolecular FRET reporters with different designs. Here we report the engineering of brighter and more photostable variants, mClover3 and mRuby3. mClover3 improves photostability by 60% and mRuby3 by 200% over the previous generation of fluorophores. Notably, mRuby3 is also 35% brighter than mRuby2, making it both the brightest and most photostable monomeric red FP yet characterized. Furthermore, we developed a standardized methodology for assessing FP performance in mammalian cells as stand-alone markers and as FRET partners. We found that mClover3 or mRuby3 expression in mammalian cells provides the highest fluorescence signals of all jellyfish GFP or coral RFP derivatives, respectively. Finally, using mClover3 and mRuby3, we engineered an improved version of the CaMKIIα reporter Camuiα with a larger response amplitude.