Aggressive development of renewable electricity sources will require significant expansions in transmission infrastructure. We present a stochastic two-stage optimisation model that captures the multistage nature of transmission planning under uncertainty and use it to evaluate interregional grid reinforcements in Great Britain (GB). In our model, a proactive transmission planner makes investment decisions in two time periods, each time followed by a market response. Uncertainty is represented by economic, technology, and regulatory scenarios, and first-stage investments must be made before it is known which scenario will occur. The model allows us to identify expected cost-minimising first-stage investments, as well as estimate the value of information, the cost of ignoring uncertainty, and the value of flexibility. Our results show that ignoring risk in planning transmission for renewables has quantifiable economic consequences, and that considering uncertainty can yield decisions that have lower expected costs than traditional deterministic planning methods. In the GB case, the value of information and cost of disregarding uncertainty in transmission planning were of the same order of magnitude (approximately £100M, in present worth terms). Further, the best plan under a risk-neutral decision criterion can differ from the best under risk-aversion. Finally, a traditional sensitivity analysis-based robustness analysis also yields different results than the stochastic model, although the former's expected cost is not much higher.