Despite being some of the most luminous objects in the universe, quasars are not well understood. Only a fraction of quasars are radio-loud, and it is not clear whether this dichotomy represents two populations of quasars with different underlying radio emission mechanisms. The effects of gravitational lensing allow the radio-quiet quasar population to be studied where they would otherwise be too faint to detect. In this thesis, four gravitationally-lensed radio-quiet quasars are observed with e-MERLIN: HS 0810+2554, RX J0911+0551, SDSS J1330+1810 and SDSS J1251+3925. HS 0810+2554 is detected at a high level of significance, the other sources are not detected. A spectral index of alpha = -0.55 +/- 0.1 is derived for HS 0810+2554, consistent with the existence of a milliarcsecond-scale jet from an AGN. A spectral index of alpha > -0.5 can be inferred from the observation of RX J0911+0551. It is not clear to what extent the source is consistent with jet emission, as it may be due to obscured AGN jets or starburst activity. Intrinsic fluxes of the lensed sources are inferred, which allow extension of the quasar optical-radio relation down to the muJy level. The observations are part of a joint effort to address the nature of the radio emission from radio-quiet quasars, the analysis of which is discussed concurrently with results of JVLA observations of HS 0810+2554 and RX J0911+0551.
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