Lightweight porous ceramic materials that can recover their shapes after mechanical deformation have numerous applications. However, these types of materials tend to be highly fragile and often crack when compressed. Here, we report on the fabrication and characterization of highly porous, freestanding composites of hexagonal boron nitride (h-BN) and single-walled carbon nanotubes (SWCNTs) of density 13-15 mg mL(-1), which corresponds to a volume fraction of 0.009, that were mechanically robust and recovered their original shape even after uniaxially compressing them by more than 50%. We made these porous elastomeric composites using a solution based assembly process that involved first shaping SWCNTs into porous networks of density ∼7 mg mL(-1) (volume fraction ∼0.005) followed by coatings of SWCNT networks with 6-8 mg mL(-1) of h-BN (volume fraction ∼0.003-0.004). The h-BN coating strengthened the underlying SWCNT networks, likely via reinforcement of the nodes between the SWCNTs, resulting in an increase in Young's modulus by ∼100% compared to that of SWCNT networks alone. Surprisingly, SWCNT networks, which were initially highly fragile, became elastomeric after h-BN coating, even though porous structures solely from h-BN are very brittle. Our fabrication approach preserves the morphology of the underlying networks, allowing for fabrication of various shapes and sizes of porous composites of h-BN and SWCNTs. Finally, our fabrication scheme is robust and facile for the preparation of porous composites of diverse ceramic materials and SWCNTs using the appropriate ceramic-precursor.