Instrumented indentation testing was used to evaluate the changes in mechanical properties of single-walled carbon nanotube composite specimens with varying weight percentage (0, 0.1, 0.5, and 1.0 wt%) of nanotubes using a low-viscosity liquid epoxy resin. The nanotubes were prepared using laser ablation technique. Reference tensile tests were also performed on the same samples, and relevant comparisons with indentation results were made. The variations in modulus and hardness obtained using nanoindentation (considering time effects) showed quantifiable differences between the various composite specimens, but differed from tensile test data. The small changes in the observed stiffness and breaking strength of carbon nanotube composites was due to the formation of bundles, their curvy morphology, and microporosity in the specimens. Interesting fluctuations obtained from the interpreted values of modulus with depth of indentation is attributed to varying degrees of the local confining effect of nanotube bundles. Creep exponents for these nanocomposites were also evaluated and indicate considerable improvements.