Soft energy storage devices, such as supercapacitors, are an essential component for powering integrated soft microsystems. However, conventional supercapacitors are mainly manufactured using hard/brittle materials that easily crack and eventually delaminate from the current collector by mechanical deformation. Therefore, to realize all-soft supercapacitors, the electrodes should be soft, stretchable, and highly conductive without compromising the electrochemical performance. This paper presents all-soft supercapacitors for integrated soft microsystems based on gallium–indium liquid metal (eutectic gallium–indium alloy, EGaIn) electrodes with integrated functionalized carbon nanotubes (CNTs). Oxygen functional groups on the surface of the CNTs ensure strong adhesion between the functionalized CNTs and the thin native oxide layer on the surface of EGaIn, which enables delamination-free soft and stretchable electrodes even under mechanical deformation. The electrochemical performances of fabricated all-soft supercapacitors in a parallel-plate arrangement were investigated without and with applied mechanical deformation. The fabricated supercapacitors exhibit areal capacitances as high as 12.4 mF cm–2 and show nearly unchanged performance under 30% applied strain. They maintain >95% of their original capacitance after >4200 charging and discharging cycles with a periodic applied strain of 30%. Finally, fabricated supercapacitors have been successfully integrated with a commercial light-emitting diode to demonstrate an integrated soft microsystem.