Electric field-activated electroactive polymers (EAPs) are an attractive class of smart materials that exhibit electromechanical coupling conversion. However, they require high actuation voltages, have low blocked stresses and low operating temperatures. These current limitations are linked to inherent polymer properties such as low dielectric constant and low modulus. Our recent efforts in EAP-based nanocomposites focus on incorporating single walled carbon nanotubes (SWNTs) to significantly improve their electromechanical response. SWNTs have shown great promise as fillers in polymer-based composites, especially in terms of improving mechanical, electrical and thermal properties. In this research we evaluate the effect of single walled carbon nanotubes (SWNTs) on the electromechanical response of polymers with varying polar nature, from non-polar to highly polar. The electric, dielectric and electromechanical strain response is studied as a function of SWNT content and polymer matrix. The electromechanical response is found to be electrostrictive and it increases with SWNT content and polarity of the matrix. Dielectric measurements are also used to measure the enhanced polarization in the nanocomposites due to the presence of SWNTs.