Banks often rely on collateralised intraday liquidity from the central bank in order to be able to effect payments in a real-time gross settlement (RTGS) payment system. If a bank is holding insufficient eligible collateral in a particular country, and therefore cannot obtain credit from the local central bank, it may have to delay payments. This constitutes a liquidity risk to the system. Furthermore, a bank operating in multiple systems may face a mismatch between the location of its collateral holdings and liquidity needs. In this paper, we examine the extent to which the liquidity risk arising from such a mismatch may be mitigated by allowing cross-border use of collateral. We develop a two-country, two-bank model in which risk-neutral banks minimise expected costs with respect to their collateral choice in each country. In our baseline model, in which each bank faces a liquidity need in only one country, we find that liquidity risk is indeed reduced by cross-border use of collateral. This result holds despite the fact that banks may find it optimal to economise on their total holdings of collateral. However, when we extend the model to allow for the possibility that a bank faces liquidity needs in both countries simultaneously, the total quantum of collateral held is important. Indeed, when a bank finds it optimal to reduce its total holdings, there may be an increase in liquidity risk in at least one country when simultaneous liquidity demands are realised.