Satellite altimetry continues to revolutionize ocean science, enabling precise observations of geocentric sea level with near-global coverage. However, altimetry has traditionally been challenged in the coastal zone (within 20 km of land) due to the presence of land in the altimeter and radiometer footprint. As the oceans further encroach on coastal communities, a more detailed understanding of the physical processes impacting sea-level variability as it propagates landward is needed. State-of-the-art satellite altimeters have the potential to observe this coastal data gap and improve our scientific understanding. Sentinel-6/Michael-Freilich (S6/MF) not only continues the decades-long record of radar altimetry in conventional low-resolution mode, but acquires data high-resolution data simultaneously in synthetic aperture radar mode. While previous ESA missions have shown the potential of high-resolution mode to improve returns at the coast, the data from S6/MF has yet to be fully explored. Complementing these measurements, the laser altimeter onboard the ICESat-2 satellite observes geocentric sea level with a much smaller footprint than radar altimeters (nominally 17 m vs ~300 m for S6/MF). ICESat-2 returns are available very close to the coast, albeit at reduced temporal resolution relative to S6/MF. Here we use these sensors in conjunction to investigate coastal sea-level trends and variability. We first perform comparisons with temporally overlapping Jason-3 data and in-situ tide gauge observations. Along shorelines of good agreement, we investigate how monthly variability propagates from the open ocean to the coast. Where differences in coastal and open-ocean variability are evident, we perform analysis to disentangle physical drivers, including riverine and atmospheric forcing, and to understand the role of coastal zone morphology. We are specifically interested in the alongshore sea-level gradient. We investigate how the gradient evolves in time, and from the coast to the open ocean. We rely primarily on correlation analysis, but leverage theoretical principles to elucidate our findings.