Programmable arrays of neutral atoms trapped in optical tweezers and lattices have emerged as a powerful tool for studies of competitive optical atomic clocks, as well as the generation of entangled quantum states with the use of Rydberg interactions and methods from both analog quantum simulation and digital quantum information processing. In this talk, I will discuss our efforts to merge these two capabilities and use Rydberg interactions to generate entanglement that can be applied to optical-frequency measurements on a platform compatible with state-of-the-art frequency precision. First, I will describe work in which we create spin squeezed states with almost 4 dB of metrological gain. We use these states to perform synchronous optical-frequency comparisons between independent ensembles of atoms in our array and realize a fractional-frequency stability of 1.087(1)10^-15 after one second of averaging time. This stability represents a 1.94(1) dB improvement over the theoretically achievable precision for this measurement when performed with the same number of unentangled atoms, known as the standard quantum limit. Second, I will present results on generating Greenberger-Horne-Zeilinger (GHZ) states on the clock transition in strontium. We investigate the possibility of leveraging cascades of GHZ states with different sizes for performing measurements that might outperform comparable classical states, even in the presence of frequency noise that would typically lead to phase excursions beyond the invertible regime for the largest GHZ states.