The Penning trap mass spectrometer SHIPTRAP at GSI is presently the only one of its kind worldwide where direct high-precision mass measurements of the heaviest elements are performed. In pioneering experiments on nobelium and lawrencium isotopes the strength of shell effects around the deformed subshell closure at N = 152 has been studied with SHIPTRAP. In order to extend these measurements to heavier elements with even lower production rate several improvements are being implemented. A new cryogenic gas stopping cell has recently been commissioned yielding a two times higher extraction efficiency when operated at 40 K. In addition, a novel method for high-precision mass measurements, the phase-imaging ion-cyclotron-resonance method (PI-ICR), has been developed. It provides an increase in resolving power by a factor of forty and a gain in precision by a factor of five. This performance opens the door for mass measurements with very high precision, relevant, for example, in the context of neutrino physics. In a recent experiment we have measured the mass difference of 187Re and 187Os with a precision of 30 eV. Our result is in good agreement with results obtained using micro-calorimeters and resolves a long-standing discrepancy in the literature. In my presentation I will review the experiments in the nobelium region, address the technical developments, and discuss some recent PI-ICR results.