If I understood your question correctly then it is simple. Consult the attached screenshot below.

That method works for a standard linear model, not a robust model. When I use rlm to generate my model (I have a few outliers in my dataset hence the need for this), the confint method just gives me NA values for confidence intervals. Screenshot attached:

You can use parametric bootstrap for this purpose. I have code for this. Let me know if you are interested.

I'm interested, could you send it to me with a quick pointer on how to implement it?

Here is a pdf with code and result. The main reference is

Davison, A. C. & Hinkley, D. V. Bootstrap methods and their application Cambridge University Press, 1997, 592 p.

The Jackknife method (https://en.wikipedia.org/wiki/Jackknife_resampling) can be applied for many estimation methods to estimate the standard error. And the confidence intervals can be approximated usually by a normal distribution.

Rohan -

I haven't used R, but aren't there different robust models under "rlm" in R?  In any case, if you are looking at a confidence interval for predicted y, that is actually a prediction interval.  You can form it in the same manner, but it is about a predicted value for y, not a point estimate, and you can use the square root of the estimated variance of the prediction error the same way you would a standard error in a confidence interval.

Cheers - Jim

PS - At the attached URL below is a weighted least squares example, where the heteroscedasticity is that of the classical ratio estimator, and estimated prediction intervals, which are vertical about predicted y-values, for regression through the origin here, are used to form prediction bounds around the regression line. 

https://www.researchgate.net/publication/263265199_CRE_Prediction_%27Bounds%27_and_Graphs_Example_for_Section_4_of_Properties_of_WLS_article

Data CRE Prediction 'Bounds' and Graphs Example for Section 4 of ...

I think if you are doing a research, it is important to describe why the CIs for model parameters are needed. Perhaps, you want to compare two models having various sets of regressors. Then you can perform out-of-sample evaluation instead of drawing conclusions based on CIs calculated only very approximately.

Just a few things to keep in mind:

You can have confidence intervals around regression coefficients, but for the estimator y, you are looking at a prediction interval.  Looking at references, that distinction may not always be remembered.

A confidence interval, or prediction interval, may be interpretable in a practical sense, but beware of p-values.  Here is a press release from the American Statistical Association:

http://www.amstat.org/newsroom/pressreleases/P-ValueStatement.pdf

As noted by Andrey, validation using separate data, not used in model selection, may be helpful. 

Finally, the attached looks like it might be of some interest here: 

R Data Analysis Examples: Robust Regression, idre, UCLA 

http://www.ats.ucla.edu/stat/r/dae/rreg.htm

I've always done this by bootstrapping. John Fox's appendix on this is a good intro.

https://socserv.socsci.mcmaster.ca/jfox/Books/Companion/appendix/Appendix-Bootstrapping.pdf

I'm still going through all the resources posted in the answers here, I can't thank you all enough!

Hye Rohan,

We are having the same problem. I still cannot manage to get the confidence interval . How about you? 

#You may try the following code.

Mymodel1