I have a timestamp in one data frame that I am trying to match to the closest timestamp in a second dataframe, for the purpose of extracting data from the second dataframe.
You can try data.tables rolling join using the "nearest" option
library(data.table) # v1.9.6+
setDT(reference)[data, refvalue, roll = "nearest", on = "datetime"]
# [1] 5 7 7 8
                                                                        I wondered if this would be able to match a data.table solution for speed, but it's a base-R vectorized solution which should outperform your apply version. And since it doesn't actually ever calculate a distance, it might actually be faster than the data.table-nearest approach. This adds the length of the midpoints of the intervals to either the lowest possible value or the starting point of the the intervals to create a set of "mid-breaks" and then uses the findInterval function to process the times. That creates a suitable index into the rows of the reference dataset and the "refvalue" can then be "transferred" to the data-object.
 data$reefvalue <- reference$refvalue[
                      findInterval( data$datetime, 
                                     c(-Inf, head(reference$datetime,-1))+
                                     c(0, diff(as.numeric(reference$datetime))/2 )) ]
 # values are [1] 5 7 7 8