If you have a grid of humidity data H that correspond to the 2.5 degree resolution coordinates lat and lon, then you just need to define the 0.25 degree resolution coordinates, let's call them lat2 and lon2. If you already have the high-res coordinate grid, great. Otherwise, an easy way to create such a grid is with cdtgrid from the Climate Data Toolbox for Matlab.
[lat2,lon2] = cdtgrid(0.25);
creates a quarter-degree resolution global grid. Then use interp2* with longitudes as the x values and latitudes as the y values:
H2 = interp2(lon,lat,H,lon2,lat2);
* Note that interpolating from coarse resolution to fine resolution as you're doing is straightforward, but if you interpolate from fine resolution to coarse resolution, you'd want to lowpass filter the high-res grid first to prevent aliasing. One such way to do that would be to use the filt2 function in CDT with a filter wavelength of twice the new resolution.