limit of added noise by a phase-preserving amplifier is the standard quantum limit, often expressed as noise temperature Tq=ℏω/2kB. Towards the goal of the quantum limit, we have developed an amplifier based on intrinsic negative resistance of a selectively damped Josephson junction. Here we present measurement results on previously proposed wide-band microwave amplification and discuss the challenges for improvements on the existing designs. We have also studied flux-pumped metamaterial-based parametric amplifiers, whose operating frequency can be widely tuned by external DC-flux, and demonstrate operation at 2ω pumping, in contrast to the typical metamaterial amplifiers pumped via signal lines at ω.