We evaluate the outage probability (OP) for L-branch equal gain combining (EGC) receivers operating over fading channels, i.e. equivalently the cumulative distribution function (CDF) of the sum of the L channel envelopes. In general, closed form expressions of OP values are out of reach. The use of Monte Carlo (MC) simulations is not a good alternative as it requires a large number of samples for small values of OP. In this paper, we use the concept of importance sampling (IS), being known to yield accurate estimates using fewer simulation runs. Our proposed IS scheme is based on sample rejection where the IS density  is the truncation of the underlying density over the $L$ dimensional sphere. It assumes the knowledge of the CDF of the sum of the L channel gains in closed-form. Such an assumption is not restrictive since it holds for various challenging fading models. We apply our approach to the case of independent Rayleigh, correlated Rayleigh, and independent and identically distributed Rice fading models. Next, we extend our approach to the interesting scenario of generalised selection combining receivers combined with EGC under the independent Rayleigh environment. For each case, we prove the desired bounded relative error property. Finally, we validate these theoretical results through some selected experiments. ​