Motivated by applications in mobile optical sensing, ultracompact high‐resolution integrated spectrometers have attracted much interest. Here, a high‐resolution integrated speckle spectrometer, comprising a linear coherent network formed by mutually coupled Mach–Zehnder interferometers and nonidentical microring resonators, is proposed and demonstrated. Deep‐etched grating lines used as mirrors on the edges of the coherent network increase the effective optical path lengths. The speckle spectrometer is realized on a silicon nitride platform, operating at 776 nm central wavelength. The eight‐in−eight‐out linear coherent network provides 64 physical channels. Fine spectral lines separated by 20 pm are experimentally resolved within a device footprint of 520 µm × 220 µm. Compressive sensing is achieved for sparse spectra over a wide optical bandwidth. Up to 600 distinctive wavelength channels can be reconstructed from the 64 physical channels, giving 12 nm operating bandwidth. Both sparse spectra and continuous spectra are well reconstructed experimentally. The integrated speckle spectrometer has great potential for use in future biosensing and bioimaging applications where high spectral resolution is desired. An integrated speckle spectrometer is proposed by using an integrated linear coherent network formed by mutually coupled Mach–Zehnder interferometers and microring resonators. On‐chip mirrors and nonidentical rings are used to create a rapid decorrelation of the speckle pattern and thus provide high spectral resolution.