Intersection of two genomic ranges to keep metadata
Presuming you don't have cases of multiple ovelaps

&gt; library(GenomicRanges)
&gt; gr1 = GRanges(c("chrI", "chrI"), IRanges(start=c(1, 101), width=c(100, 100)), mcols=data.frame(foo=c(0.1, 0.2)))
&gt; gr2 = GRanges(c("chrI"), IRanges(start=c(50), width=c(101)))
&gt; o = findOverlaps(gr1, gr2)
&gt; grl1 = split(gr1[queryHits(o)], 1:length(o)) # You can't mendoapply on a GRanges object
&gt; grl2 = split(gr2[subjectHits(o)], 1:length(o))
&gt; foo = function(x, y) {
+     rv = x
+     start(rv) = max(start(x), start(y))
+     end(rv) = min(end(x), end(y))
+     return(rv)
+ }
&gt; unlist(mendoapply(foo, grl1, y=grl2))


The output is:

GRanges object with 2 ranges and 1 metadata column:
    seqnames     ranges strand | mcols.foo
       &lt;Rle&gt;  &lt;IRanges&gt;  &lt;Rle&gt; | &lt;numeric&gt;
  1     chrI [ 50, 100]      * |       0.1
  2     chrI [101, 150]      * |       0.2
  -------
  seqinfo: 1 sequence from an unspecified genome; no seqlengths


It'd be more memory efficient to iterate over o, but this gives you the idea.

In cases of multiple overlaps, one could use intersect(), then findOverlaps() with that and then continue on with the procedure demonstrated above (or iterate over the overlaps).