Finding natural food coloring options from plant-based sources to substitute artificial dyes is a challenging task because natural dyes often present low water-solubility, not very vibrant hues, and instability due to interactions with food ingredients. Chemometric approaches can be used to evaluate color differences and patterns resulting from natural and synthetic dyes when applied to food systems. Here, the Mixture Design and the Principal Component Analysis (PCA) were applied to evaluate the substitution of the following artificial food dyes: yolk yellow, apricot yellow, strawberry red, and tartrazine by natural dyes (water-soluble curcumin, yellow shade; Hibiscus sabdariffa extract, red shade; Spirulina platensis extract, blue/green shade), in three food simulated systems (phosphate buffer, pH 6.9; yogurt, pH 4.0 and citrate buffer, pH 3.0). The color parameters L*, a*, b*, C* and °h were determined and color difference (ΔE*) with artificial dyes resulted in 11 empirical models. PCA yielded a clear map for the identification of the closely matches natural/artificial dyes for the food simulated systems in three subregions. Furthermore, the antioxidant capacity of the natural dyes was determined by OxHLIA and TBARS. It was possible to make an assessment guide that may be useful for other food systems and dyes. •Curcumin, hibiscus and spirulina are great sources of natural dyes.•Color difference (ΔE*) between their blends and artificial dyes was evaluated.•Mixture experimental design yielded empirical models to describe ΔE*.•Principal Component Analysis yielded a visual tool to identify color proximity.•Curcumin, hibiscus and spirulina showed antioxidant action in OxHLIA/TBARS assays.