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We present a spectral analysis of NuSTAR and NICER observations of the luminous, persistently accreting neutron star (NS) low-mass X-ray binary Cygnus X-2. The data were divided into different branches that the source traces out on the Z-track of the X-ray color-color diagram; namely the horizontal branch, normal branch, and the vertex between the two. The X-ray continuum spectrum was modeled in two different ways that produced a comparable quality fit. The spectra showed clear evidence of a reflection component in the form of a broadened Fe K line, as well as a lower energy emission feature near 1 keV likely due to an ionized plasma located far from the innermost accretion disk. We account for the reflection spectrum with two independent models (relxillns and rdblur*rfxconv). The inferred inclination is in agreement with earlier estimates from optical observations of ellipsoidal light curve modeling (relxillns: $i=67^{\circ}\pm4^{\circ}$, rdblur*rfxconv: $i=60^{\circ}\pm10^{\circ}$). The inner disk radius remains close to the NS ($R_{\rm in}\leq1.15\ R_{\mathrm{ISCO}}$) regardless of the source position along the Z-track or how the 1 keV feature is modeled. Given the optically determined NS mass of $1.71\pm0.21\ M_{\odot}$, this corresponds to a conservative upper limit of $R_{\rm in}\leq19.5$ km for $M=1.92\ M_{\odot}$ or $R_{\rm in}\leq15.3$ km for $M=1.5\ M_{\odot}$. We compare these radius constraints to those obtained from NS gravitational wave merger events and recent NICER pulsar light curve modeling measurements.