The efficacy of helium (He) and argon (Ar) plasma jets are being investigated for different healthcare applications including wound and cancer therapy, sterilisation and surface disinfections. Current research points to a potential link between the generation of reactive oxygen and nitrogen species (RONS) and outcomes in a range of biological and medical applications. As new data accrue, further strengthening this link, it becomes important to understand the controlled delivery of RONS into solutions, tissue fluids and tissues. This paper investigates the use of He and Ar plasma jets to deliver three RONS (hydrogen peroxide—H2O2, nitrite—$\text{NO}_{2}^{-}$ and nitrate—$\text{NO}_{3}^{-}$ ) and molecular oxygen (O2) directly into deionised (DI) water, or indirectly into DI water through an agarose target. The DI water is used in place of tissue fluid and the agarose target serves as a surrogate of tissue. Direct plasma jet treatments deliver more RONS and O2 than the through-agarose treatments for equivalent treatments times. The former only deliver RONS whilst the plasma jets are ignited; the latter continues to deliver RONS into the DI water long after the plasmas are extinguished. The He plasma jet is more effective at delivering H2O2 and $\text{NO}_{2}^{-}$ directly into DI water, but the Ar plasma jet is more effective at nitrating the DI water in both direct and through-agarose treatments. DI water directly treated with the plasma jets is deoxygenated, with the He plasma jet purging more O2 than the Ar plasma jet. This effect is known as 'sparging'. In contrast, for through-agarose treatments both jets oxygenated the DI water. These results indicate that in the context of direct and indirect plasma jet treatments of real tissue fluids and tissue, the choice of process gas (He or Ar) could have a profound effect on the concentrations of RONS and O2. Irrespective of operating gas, sparging of tissue fluid (in an open wound) for long prolonged periods during direct plasma jet treatment, could have implications for healthy tissue function; whilst through-tissue plasma jet treatment may provide a method to reperfuse oxygen-starved tissue. The assays described in this paper can be readily adopted (by others) and may support the future development of plasma sources to deliver specific (metered) doses of RONS.