This work proposes two deep eutectic solvents (DESs) based on lithium bis(fluorosulfonyl)imide and sodium bis(fluorosulfonyl)imide together with N-methylacetamide and formamide as electrolytes for activated carbon (AC) electrochemical double-layer capacitors (EDLCs) at 25 °C. The formulated DESs exhibit a large electrochemical window (ΔE > 2.5 V), good thermal stability (∼150 °C) and ionic conductivity (3–4 mS cm−1), and moderate viscosity (11.3 mPa s). Through the Vogel–Tamman–Vulcher fitting equation, the evolution of pseudo-energy activation was delineated with respect to the nature of the H-bond donor or alkali salt. These electrolytes present a superionic character gleaned from the Walden classification, and their ionicity exceeds that of standard organic electrolytes based on similar alkali salts. The performance of the AC-based EDLC was assessed by cyclic voltammetry, electrochemical impedance spectroscopy, and galvanostatic charge/discharge, yielding 140 F g−1 with an 8% capacity retention during 200 h of floating. Based on the physicochemical properties and electrochemical performance of these DESs, they represent a promising green-alternative electrolyte for supercapacitor applications.