The SNP heritability estimates for IQ of (h^2 = ~0.2) are primarily based on a low quality test that has a test-retest reliability of 0.6, compared to ~0.9 for a gold-standard IQ test. So a simple calculation to adjust for this gets you a predicted SNP heritability of 0.2 * (0.9 / 0.6)^2 = 0.45 0.2 * (0.9 / 0.6) = 0.30 for a gold standard IQ test, which matches the SNP heritability of height. As for the rest of the missing heritability: variants with frequency less than 1% aren’t accounted for by the SNP heritability estimate, and they might contribute a decent bit if there are lots of them and their effects sizes are larger.
EDIT: the original adjustment for test-retest reliability was incorrect: the correlations shouldn’t be squared.
Using finemapping. I.e. assuming a model where nonzero additive effects are sparsely distributed among SNPs, you can do Bayesian math to infer how probable each SNP is to have a nonzero effect and its expected effect size conditional on observed GWAS results. Things like SnpEff can further help by giving you a better prior.