We predict cosmological constraints for forthcoming surveys using Superluminous Supernovae (SLSNe) as standardisable candles. Due to their high peak luminosity, these events can be observed to high redshift (z~3), opening up new possibilities to probe the Universe in the deceleration epoch. We describe our methodology for creating mock Hubble diagrams for the Dark Energy Survey (DES), the Search Using DECam for Superluminous Supernovae (SUDSS) and a sample of SLSNe possible from the Large Synoptic Survey Telescope (LSST), exploring a range of standardisation values for SLSNe. We include uncertainties due to gravitational lensing and marginalise over possible uncertainties in the magnitude scale of the observations (e.g. uncertain absolute peak magnitude, calibration errors). We find that the addition of only ~100 SLSNe from SUDSS to 3800 Type Ia Supernovae (SNe Ia) from DES can improve the constraints on w and Omega_m by at least 20% (assuming a flat wCDM universe). Moreover, the combination of DES SNe Ia and 10,000 LSST-like SLSNe can measure Omega_m and w to 2% and 4% respectively. The real power of SLSNe becomes evident when we consider possible temporal variations in w(a), giving possible uncertainties of only 2%, 5% and 14% on Omega_m, w_0 and w_a respectively, from the combination of DES SNe Ia, LSST-like SLSNe and Planck. These errors are competitive with predicted Euclid constraints, indicating a future role for SLSNe for probing the high redshift Universe.
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