X-ray bursts are among the most common and spectacular astrophysical phenomena, where huge spikes in X-ray emissions occur as a result of thermonuclear explosions on the surface of an accreting neutron star. The extreme temperatures and densities present during bursts feed a new set of nuclear reactions known as the rp (rapid proton) process, where consecutive rapid proton captures produce proton-rich unstable nuclei up to the A ∼ 100 mass region. Advancements in space-based X-ray astronomy have produced a wealth of observational data on Type-I X-ray bursts, which, paired with recent advances in computational power, have allowed for sophisticated models to be produced, thereby increasing our understanding of these astrophysical scenarios. However, present simulations are ultimately limited by uncertainties in the stellar reaction rate of key nuclear reactions, and consequently questions remain in relation to the resulting light curve and final burnt ashes. The ⁴⁸Cr(p,γ) and ⁵⁹Cu(p,γ) radiative proton-capture reactions are expected to be of considerable importance in their effect on energy generation in Type-I X-ray burst environments. Previous studies have indicated that the rate of these stellar reactions is dominated by resonant capture to excited states above the proton-emission threshold. However, due to uncertainties in the properties of key proton-unbound resonances of the final systems ⁴⁹Mn and ⁶⁰Zn respectively, the stellar reaction rate of each reaction is not well determined. Consequently, by determining the nuclear properties of these levels in each final system, it is possible to estimate and subsequently constrain the uncertainties of the ⁴⁸Cr(p,γ) ⁴⁹Mn and ⁵⁹Cu(p,γ) ⁶⁰Zn stellar reaction rates. In this thesis work, excited states in ⁴⁹Mn and ⁶⁰Zn were populated by indirect measurements that involve two different reaction mechanisms, and were subsequently studied using techniques in γ-ray spectroscopy. The properties of resonant states in ⁴⁹Mn were determined via the ¹¹B(⁴⁰Ca,2n) fusion-evaporation reaction at the ATLAS (Argonne Tandem Linear Accelerator System) facility of Argonne National Laboratory (ANL). The properties of resonant states in ⁶⁰Zn were determined via the d( ⁵⁹Cu,n) transfer reaction at the FRIB (Facility for Rare Isotope Beams) facility at Michigan State University (MSU). The analysis shown here represents the first identification of a number of low-spin, proton-unbound levels in both ⁴⁹Mn and ⁶⁰Zn, which correspond to key astrophysical resonances in the ⁴⁸Cr + p and the ⁵⁹Cu + p systems, respectively. In particular, an ℓ = 0 resonance and an ℓ = 1 resonance were identified at E_r = 482.9(84) keV and 507.9(83) keV, respectively in ⁴⁹Mn, while two predominantly ℓ = 1 resonances were identified at E_r = 770.4(36) keV and 1150(13) keV in ⁶⁰Zn. These resonances were found to dominate the respective ⁴⁸Cr(p,γ) and ⁵⁹Cu(p,γ) stellar reaction rates over the X-ray burst temperature range, thereby reducing the associated uncertainty in each by several orders of magnitude.