Global networks of tide gauges for the "historical" sea level, which gets us back relatively accurately to at least the late 1800s. There are a variety of geologic records of sea level which we can use to build sea level curves going back well beyond historical periods.

> The same question has bothered me about climate measurements which in the past were not digital and inaccurate

If you want a deep dive on this, starting with something like the 'physical science basis' product of the latest IPCC report would be a good start. The short version is that we can place individual temperature records into context with a vast numbers of proxy data that allow us to reconstruct temperature (e.g., oxygen isotopes, clumped isotopes, compound specific isotopes, tree rings, etc.) and climate modeling that all tell us effectively the same thing.